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ThreeColumnLayout_wrapper__gPK_l"> <div class="ant-col ThreeColumnLayout_leftColumn__yqNgV"> <div> <div> <div id="article-table-of-contents" data-ismobile="false"> <div class="TableOfContents_tableOfContents__0jAuv"> <div class="TableOfContents_tableOfContents__title__CH9Lz"> 在这一页上</gydF4y2Badiv> <a class="TableOfContents_tableOfContents__item__JJil1" href="#abstract">文摘</gydF4y2Baa> <a class="TableOfContents_tableOfContents__item__JJil1" href="#introduction">介绍</gydF4y2Baa> <a class="TableOfContents_tableOfContents__item__JJil1" href="#references">引用</gydF4y2Baa> <a class="TableOfContents_tableOfContents__item__JJil1" href="#copyright">版权</gydF4y2Baa> <a class="TableOfContents_tableOfContents__item__JJil1" href="#related-articles">相关文章</gydF4y2Baa> </div> </div> </div> </div> </div> <div class="ant-col ThreeColumnLayout_middleColumn__sbd41"> <div class="ArticleMiddleSection_articleMiddleSection__gAv9z"> <div class="articleHeader"> <div class="articleHeader__specialIssue"> <span class="articleHeader__specialIssue_tag">特殊的问题</年代pan> <h2 class="articleHeader__specialIssue_title">应用计量经济学的进步</gydF4y2Bah2> <a href="//www.newsama.com/journals/jps/si/982398/" class="articleHeader__specialIssue_url" target="_blank" rel="noreferrer">把这个特殊的问题</gydF4y2Baa> </div> <strong>评论文章|<gydF4y2Ba!-- -->开放获取</年代trong> <div class="articleHeader__meta"> <span>体积<gydF4y2Ba!-- -->2011年<gydF4y2Ba!-- -->|</年代pan> <span>文章的ID<gydF4y2Ba!-- -->691058年<gydF4y2Ba!-- -->|</年代pan> <span class="articleHeader__meta_doiLink"><a href="https://doi.org/10.1155/2011/691058" aria-label="Doi-link" target="_blank" rel="noreferrer">https://doi.org/10.1155/2011/691058</gydF4y2Baa></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示引用</gydF4y2Babutton> </div> <h1 class="articleHeader__title">CSS和两步SARFIMA模型中参数估计的方法</gydF4y2Bah1> <div class="articleHeader__authors"> <span class="articleHeader__authors_author"><strong>Erol Egrioglu</年代trong><a href="//www.newsama.com/cdn-cgi/l/email-protection" aria-label="Mail Option"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a>,<年代up>1</年代up></span> <span class="articleHeader__authors_author">Cagdas哈坎Aladag<gydF4y2Ba!-- -->,<年代up>2</年代up></span> <span class="articleHeader__authors_author">和<gydF4y2Ba!-- -->杰姆Kadilar<年代up>2</年代up></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示更多</gydF4y2Babutton> </div> <div class="articleHeader__academicEditor"> <strong>学术编辑器:</年代trong> <span>迈克Tsionas</年代pan> </div> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</年代trong> <span>2011年5月19日</年代pan> </div> <div class="articleHeader__timeline_item "> <strong>接受</年代trong> <span>2011年7月01</年代pan> </div> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</年代trong> <span>2011年8月14日</年代pan> </div> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</gydF4y2Bah4> <p>季节性自回归略微集成移动平均(SARFIMA)模型用于季节性memory-dependent长时间序列的分析。两种方法,有条件的平方和(CSS)和两步方法引入了霍斯金表示:(1984),提出了估算SARFIMA模型的参数。然而,在文献中没有进行模拟研究。因此,尚不清楚这些方法如何在不同参数设置和样本大小SARFIMA模型。本研究的目的是指由模拟研究这些方法的行为。根据仿真的结果,不同参数设置下两种方法的优缺点,讨论了样本大小通过比较均方根误差(RMSE)通过CSS和两步方法。的结果比较,发现CSS方法产生比从两步方法获得更好的结果。</pgydF4y2Ba> <span class="end-abs"></span> <h4 id="introduction">1。介绍</gydF4y2Bah4> <p>近年来,有很多研究自回归略微集成移动平均(ARFIMA)模型在文献中。然而,大多数的时间序列在现实生活中可能有季节性,除了长期的结构。因此,SARFIMA模型被引入模型时间序列。一般来说,SARFIMA<年代vg height="14.7125" id="M1" style="vertical-align:-3.2316pt;width:109.375px;" version="1.1" viewbox="0 0 109.375 14.7125" width="109.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.277466" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.478714" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.13031" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.344061" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.070435" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.233932" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.397434" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.824215" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.025463" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.902832" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.116585" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.881424" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,11.1,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>过程中给出以下形式:<年代pan class="equation" id="EEq1"> <svg height="18.924999" id="M2" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.925)"> <g transform="translate(72,-56.86)"> <text transform="matrix(1,0,0,-1,81.42,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.518143" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.757139" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.38493" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.548428" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.750637" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; 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<tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,228.26,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,235.8,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,245.68,57.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,252.39,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> Θ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.306553" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.508759" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.747757" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.387329" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.550831" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.753036" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.004539" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,328.96,57.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,332.2,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="132.55" y="-0.63999999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="136.7135" y="-0.63999999"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="142.965" y="-0.63999999"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="146.09074" y="-0.63999999"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="152.34225" y="-0.63999999"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.3375" id="M3" style="vertical-align:-3.21404pt;width:16.512501px;" version="1.1" viewbox="0 0 16.512501 14.3375" width="16.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个时间序列,<年代vg height="10.325" id="M4" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是运营商转变,如<年代vg height="17.137501" id="M5" style="vertical-align:-3.2316pt;width:78.724998px;" version="1.1" viewbox="0 0 78.724998 17.137501" width="78.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.1375)"> <g transform="translate(72,-58.29)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.75,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.53,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-49.65,58.43)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.94,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-21.02,58.43)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7393761" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7344961" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="7.1875" id="M6" style="vertical-align:-0.13794pt;width:7px;" version="1.1" viewbox="0 0 7 7.1875" width="7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是季节性的滞后,<年代vg height="10.75" id="M7" style="vertical-align:-0.15048pt;width:9.375px;" version="1.1" viewbox="0 0 9.375 10.75" width="9.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.75)"> <g transform="translate(72,-63.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="10.325" id="M8" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>代表了季节性和季节性略微差异;分别<年代vg height="11.025" id="M9" style="vertical-align:-3.21404pt;width:11.125px;" version="1.1" viewbox="0 0 11.125 11.025" width="11.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.025)"> <g transform="translate(72,-63.18)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.39,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个白噪声过程,正态分布<年代vg height="17.799999" id="M10" style="vertical-align:-3.2316pt;width:63.837502px;" version="1.1" viewbox="0 0 63.837502 17.799999" width="63.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8)"> <g transform="translate(72,-57.76)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.803552" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.967051" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.218552" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.4198" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.18,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-29.31,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="13.55" id="M11" style="vertical-align:-2.29482pt;width:31.487499px;" version="1.1" viewbox="0 0 31.487499 13.55" width="31.487499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.064435" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.227934" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.930021" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="13.45" id="M12" style="vertical-align:-2.21957pt;width:33.337502px;" version="1.1" viewbox="0 0 33.337502 13.45" width="33.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.405376" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="13.45" id="M13" style="vertical-align:-2.21957pt;width:29.6px;" version="1.1" viewbox="0 0 29.6 13.45" width="29.6" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.5390692" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.702568" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.404655" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="13.45" id="M14" style="vertical-align:-2.21957pt;width:37.900002px;" version="1.1" viewbox="0 0 37.900002 13.45" width="37.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-67.78,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.892754" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是由<年代pan class="equation" id="eq1"> <svg height="111.4625" id="M15" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 111.4625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,111.4625)"> <g transform="translate(72,17.17)"> <text transform="matrix(1,0,0,-1,117.87,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.189999" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.14" y="-0.0099999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.303499" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.505707" y="-0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.145041" y="-0.0099999998"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.040001" y="7.1054274e-015"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.054665" y="7.1054274e-015"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.407387" y="7.1054274e-015"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,195.34,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,200.22,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.477754" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.817974" y="0"> ⋯</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.259418" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.59964" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,258.89,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,263.67,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,272.87,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,279.88,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-118.82" y="24.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-160.5" y="21.99"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-151.87292" y="21.99"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-147.70943" y="21.99"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-138.50722" y="21.99"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-130.86789" y="21.99"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-112.97" y="21.99"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-103.95534" y="21.99"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-92.602615" y="21.99"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,193.83,33.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,198.71,36.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.465251" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.817974" y="0"> ⋯</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.246918" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.59964" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,255.86,33.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,260.72,36.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,269.92,41.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,274.78,34.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.52"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-113.72" y="24.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-158.39" y="21.99"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-146.77472" y="21.99"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-142.61122" y="21.99"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-133.40901" y="21.99"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-125.76968" y="21.99"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-107.87" y="21.99"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-98.855339" y="21.99"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-87.502609" y="21.99"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,196.82,8.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,201.69,12.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,210.9,17.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,218.02,12.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> ⋯</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.121887" y="0"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,266.69,8.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,271.47,12.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,280.67,17.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2797279" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,289.3,9.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.52"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-128.24001" y="24.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-172.39999" y="21.99"> Θ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-161.29733" y="21.99"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-157.13383" y="21.99"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-147.93163" y="21.99"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-140.2923" y="21.99"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-122.39" y="21.99"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-113.37534" y="21.99"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-102.02261" y="21.99"> Θ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,196.31,-15.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,201.18,-12.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.477754" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.817974" y="0"> ⋯</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.259418" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.59964" y="0"> Θ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,260.82,-15.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,265.67,-12.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,274.87,-7.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.0084162" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,283.23,-14.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.52"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="181.52" y="-39.200001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="185.6835" y="-39.200001"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="191.935" y="-39.200001"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="195.06075" y="-39.200001"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="201.31226" y="-39.200001"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vg height="9.875" id="M16" style="vertical-align:-2.29482pt;width:22.0625px;" version="1.1" viewbox="0 0 22.0625 9.875" width="22.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.1139669" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.315215" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="12.925" id="M17" style="vertical-align:-1.90608pt;width:28.125px;" version="1.1" viewbox="0 0 28.125 12.925" width="28.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.4267821" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.62803" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>季节性和季节性的命令参数,分别。</pgydF4y2Ba> <p>柏丽[<gydF4y2Baa href="#B3">1</gydF4y2Baa>)和哈斯勒和种<gydF4y2Baa href="#B17">2</gydF4y2Baa>)检查ARFIMA模型的基本特征,而一些重大贡献SARFIMA Giraitis和Leipus提出的模型<gydF4y2Baa href="#B15">3</gydF4y2Baa>),Arteche和罗宾逊(<gydF4y2Baa href="#B2">4</gydF4y2Baa>钟),(<gydF4y2Baa href="#B9">5</gydF4y2Baa>),Velasco和罗宾逊(<gydF4y2Baa href="#B28">6</gydF4y2Baa>),Giraitis et al。<gydF4y2Baa href="#B16">7</gydF4y2Baa>),和海<gydF4y2Baa href="#B22">8</gydF4y2Baa>]。当所有的参数都是不同的从零(<gydF4y2Baa href="#EEq1">1.1</gydF4y2Baa>),当一些参数如<年代vg height="13.4125" id="M18" style="vertical-align:-2.29482pt;width:55.950001px;" version="1.1" viewbox="0 0 55.950001 13.4125" width="55.950001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4125)"> <g transform="translate(72,-61.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.1139669" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.315215" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.04159" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.255341" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.682121" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.883369" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>等于零,不同的参数估计方法相比,通过执行模拟研究在文献[<gydF4y2Baa href="#B26">9</gydF4y2Baa>- - - - - -<gydF4y2Baa href="#B23">11</gydF4y2Baa>]。</pgydF4y2Ba> <p>季节性长期结构等存在于时间序列在不同研究领域累积的钱系列Porter-Hudak [<gydF4y2Baa href="#B24">12</gydF4y2Baa>输入系列),IBM在雷<gydF4y2Baa href="#B25">13</gydF4y2Baa>],尼罗河数据Montanari et al。<gydF4y2Baa href="#B20">14</gydF4y2Baa>]。Candelon和Gil-Alana<gydF4y2Baa href="#B7">15</gydF4y2Baa>)预测在南美国家的工业生产指数采用SARFIMA模型。Gil-Alana [<gydF4y2Baa href="#B13">16</gydF4y2Baa>]发现GDP系列在德国,意大利和丹麦有一个结构是适合使用SARFIMA模型。</pgydF4y2Ba> <p>Brietzke et al。<gydF4y2Baa href="#B6">17</gydF4y2Baa>利用Durbin-Levinson算法<年代vg height="13.55" id="M19" style="vertical-align:-2.29482pt;width:149.4875px;" version="1.1" viewbox="0 0 149.4875 13.55" width="149.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5772982" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.617687" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.819895" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.860283" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.750397" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.790787" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="79.031464" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.071854" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="101.18678" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="113.22717" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>模型。雷(<gydF4y2Baa href="#B25">13</gydF4y2Baa>)修改霍斯金表示:提出的方法(<gydF4y2Baa href="#B19">18</gydF4y2Baa>),这个修改方法用于一个特殊SARFIMA过程有两种不同的季节性差异的参数。Darne et al。<gydF4y2Baa href="#B10">19</gydF4y2Baa>改编的方法,提出了ARFIMA钟和柏丽[<gydF4y2Baa href="#B8">20.</gydF4y2Baa>),SARFIMA模型。然而,CSS的属性方法用于Darne et al。<gydF4y2Baa href="#B10">19</gydF4y2Baa>)还没有被模拟研究了。</pgydF4y2Ba> <p>Arteche和罗宾逊(<gydF4y2Baa href="#B2">4</gydF4y2Baa>]介绍了一个基于谱密度函数的半参数方法在估计参数SARFIMA模型的情况<年代vg height="10.9125" id="M20" style="vertical-align:-0.17555pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 10.9125" width="35.637501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.114927" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.155315" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。加仑小时用于ARFIMA方法扩展用于SARFIMA模型<年代vg height="13.55" id="M21" style="vertical-align:-2.29482pt;width:149.4875px;" version="1.1" viewbox="0 0 149.4875 13.55" width="149.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5772982" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.617687" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.819895" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.860283" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.750397" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.790787" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="79.031464" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.071854" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="101.18678" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="113.22717" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>由Porter-Hudak [<gydF4y2Baa href="#B24">12</gydF4y2Baa>],加仑小时估计已经被Ooms修改和哈斯勒<gydF4y2Baa href="#B21">21</gydF4y2Baa>]。同时,不同的值的模拟研究<年代vg height="12.7625" id="M22" style="vertical-align:-1.76814pt;width:40.6875px;" version="1.1" viewbox="0 0 40.6875 12.7625" width="40.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.7625)"> <g transform="translate(72,-61.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.852844" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.730213" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.943966" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和样本大小进行了使用加仑小时,惠特尔和确切的最大似然(EML)莱尔森et al。<gydF4y2Baa href="#B26">9</gydF4y2Baa>,<gydF4y2Baa href="#B27">10</gydF4y2Baa>)和帕尔马和陈<gydF4y2Baa href="#B23">11</gydF4y2Baa>]。除了这些研究,提出了很多方法来确定季节性长期结构由哈斯勒和种<gydF4y2Baa href="#B18">22</gydF4y2Baa>),Gil-Alana和罗宾逊(<gydF4y2Baa href="#B14">23</gydF4y2Baa>],Arteche [<gydF4y2Baa href="#B1">24</gydF4y2Baa>],Gil-Alana [<gydF4y2Baa href="#B11">25</gydF4y2Baa>,<gydF4y2Baa href="#B12">26</gydF4y2Baa>]。</pgydF4y2Ba> <p>我们检查CSS的属性和两个评估方法的仿真研究,比较两种方法根据不同的参数设置和样本大小。在仿真研究中,一个特定形式的模型给出了(<gydF4y2Baa href="#EEq1">1.1</gydF4y2Baa>)中,<年代vg height="9.875" id="M23" style="vertical-align:-2.29482pt;width:7.7624998px;" version="1.1" viewbox="0 0 7.7624998 9.875" width="7.7624998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="10.75" id="M24" style="vertical-align:-0.15048pt;width:9.375px;" version="1.1" viewbox="0 0 9.375 10.75" width="9.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.75)"> <g transform="translate(72,-63.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="9.875" id="M25" style="vertical-align:-2.29482pt;width:7.9124999px;" version="1.1" viewbox="0 0 7.9124999 9.875" width="7.9124999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>都等于零审查通过使用CSS和两种评估方法。该模型也可以表示为SARFIMA<年代vg height="14.7125" id="M26" style="vertical-align:-3.2316pt;width:62.825001px;" version="1.1" viewbox="0 0 62.825001 14.7125" width="62.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.6689" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.88265" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.647491" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.13,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。仿真研究后,结果从CSS和两种评估方法进行了比较,并指出,获得更好的结果时,CSS方法。</pgydF4y2Ba> <p>本研究的大纲如下。部分<gydF4y2Baa href="#sec2">2</gydF4y2Baa>包含SARFIMA模型相关的简短信息。CSS的方法和两种方法解释部分<gydF4y2Baa href="#sec3">3</gydF4y2Baa>和<gydF4y2Baa href="#sec4">4</gydF4y2Baa>,分别。仿真研究的大纲和结果部分<gydF4y2Baa href="#sec5">5</gydF4y2Baa>。最后,总结了仿真研究的结果最后一节。</pgydF4y2Ba> <h4 id="sarfima-models">2。SARFIMA模型</gydF4y2Bah4> <p>当<年代vg height="9.875" id="M27" style="vertical-align:-2.29482pt;width:7.7624998px;" version="1.1" viewbox="0 0 7.7624998 9.875" width="7.7624998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="9.875" id="M28" style="vertical-align:-2.29482pt;width:7.9124999px;" version="1.1" viewbox="0 0 7.9124999 9.875" width="7.9124999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="10.75" id="M29" style="vertical-align:-0.15048pt;width:9.375px;" version="1.1" viewbox="0 0 9.375 10.75" width="9.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.75)"> <g transform="translate(72,-63.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="10.325" id="M30" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="12.925" id="M31" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在模型(设置为0<gydF4y2Baa href="#EEq1">1.1</gydF4y2Baa>),该模型称为季节性略微集成(SFI)模型。SFI模型首先介绍了Arteche和罗宾逊(<gydF4y2Baa href="#B2">4</gydF4y2Baa>),基本信息模型可以发现在柏丽<gydF4y2Baa href="#B3">1</gydF4y2Baa>]。你可以给出的模型<年代pan class="equation" id="EEq2"> <svg height="18.924999" id="M32" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.925)"> <g transform="translate(72,-56.86)"> <text transform="matrix(1,0,0,-1,163.2,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,196.94,65.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,201.29,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,205.45,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,213,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,222.87,57.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,229.58,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,247.19,57.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,250.42,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="214.33" y="-0.63999999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="218.4935" y="-0.63999999"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="224.745" y="-0.63999999"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="227.87074" y="-0.63999999"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="234.12225" y="-0.63999999"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>无限的移动平均模型的演示(<gydF4y2Baa href="#EEq2">2.1</gydF4y2Baa>)如下:<年代pan class="equation" id="EEq3"> <svg height="48.262501" id="M33" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.262501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.2625)"> <g transform="translate(72,-33.39)"> <text transform="matrix(1,0,0,-1,134.53,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,144.4,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,151.11,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> Ψ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.443125" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.606625" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,187.93,54.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.28,49.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.25" y="0.0099999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,204.09,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,210.8,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,226.86,65.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,222.84,43.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,223.36,36.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,241.08,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,250.47,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,255.71,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,261.27,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7393761" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7344961" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.585376" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,279.1,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="185.64999" y="0.2"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="189.81349" y="0.2"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="196.065" y="0.2"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="199.19075" y="0.2"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="205.44225" y="0.2"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.7125" id="M34" style="vertical-align:-3.2316pt;width:196.0625px;" version="1.1" viewbox="0 0 196.0625 14.7125" width="196.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.56,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-53.85,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.37965" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.54315" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.09544" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.435661" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.31303" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.476532" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.952366" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.115868" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.455124" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.618622" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.495995" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.659492" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="98.998756" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="103.16225" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="112.71455" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="124.06727" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="130.31877" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="134.48227" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,(<年代vg height="17.887501" id="M35" style="vertical-align:-3.2316pt;width:104.775px;" version="1.1" viewbox="0 0 104.775 17.887501" width="104.775" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.56,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-53.85,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∼</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.03,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.9140801" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.9092" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-17.25,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.815095" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.978594" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.855965" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,因为<年代vg height="10.7375" id="M36" style="vertical-align:-0.13794pt;width:51.4375px;" version="1.1" viewbox="0 0 51.4375 10.7375" width="51.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.327958" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.457067" y="0"> ∞</gydF4y2Batspan> </text> </g> </g> </svg>)。</pgydF4y2Ba> <p>无限的自回归模型的演示(<gydF4y2Baa href="#EEq2">2.1</gydF4y2Baa>)如下:<年代pan class="equation" id="EEq4"> <svg height="48.262501" id="M37" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.262501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.2625)"> <g transform="translate(72,-33.39)"> <text transform="matrix(1,0,0,-1,133.41,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Π</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.266163" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,157.89,54.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,162.24,49.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.25" y="0.0099999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,178.36,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,185.08,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,201.14,65.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,197.11,43.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,197.63,36.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,215.35,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,222.95,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,228.19,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.07,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7393761" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7344961" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.585376" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,259.37,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,276.97,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,280.21,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="184.53999" y="0.2"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="188.70351" y="0.2"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="194.955" y="0.2"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="198.08075" y="0.2"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="204.33224" y="0.2"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.7125" id="M38" style="vertical-align:-3.2316pt;width:204.52499px;" version="1.1" viewbox="0 0 204.52499 14.7125" width="204.52499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.35,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.63,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.367147" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.530645" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.082939" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.423161" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.300529" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.464027" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.939861" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.103363" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.442619" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.606117" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="86.170677" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.048042" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.21155" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="107.5508" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="111.7143" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="121.2791" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="132.61932" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="138.87082" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="143.03432" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,(<年代vg height="17.887501" id="M39" style="vertical-align:-3.2316pt;width:120.7375px;" version="1.1" viewbox="0 0 120.7375 17.887501" width="120.7375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.35,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.63,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36.82,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.9092" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="18.90432" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.04,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.815095" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.978594" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.54315" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.420521" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,因为<年代vg height="10.7375" id="M40" style="vertical-align:-0.13794pt;width:51.4375px;" version="1.1" viewbox="0 0 51.4375 10.7375" width="51.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.327958" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.457067" y="0"> ∞</gydF4y2Batspan> </text> </g> </g> </svg>)。</pgydF4y2Ba> <p>对模型(<gydF4y2Baa href="#EEq2">2.1</gydF4y2Baa>)、自协方差、自相关函数可以分别写如下:<年代pan class="equation" id="EEq5"> <svg height="83.637497" id="M41" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 83.637497" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,83.6375)"> <g transform="translate(72,-5.09)"> <text transform="matrix(1,0,0,-1,70.76,52.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.427022" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.590521" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.091841" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.868467" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.507801" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.370003" y="-8.2200003"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.533501" y="-8.2200003"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.098053" y="-8.2200003"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.349556" y="-8.2200003"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,168.27,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,173.51,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.4147587" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.578258" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.617928" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.958149" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.209648" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.274563" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 116.5,55.83 140.07,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,116.5,43.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="141.27" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.4300003" y="-0.0099999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.593499" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.14579" y="-0.0099999998"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.486012" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.13905" y="-0.0099999998"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.479267" y="-0.0099999998"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.730766" y="-0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.982269" y="-0.0099999998"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="80.409531" y="-0.0099999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.573029" y="-0.0099999998"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.600197" y="-0.0099999998"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="104.94041" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="114.49271" y="-0.0099999998"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="125.83293" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="135.89784" y="-0.0099999998"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,265.11,57.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,269.98,52.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.166139" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.418598" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.458988" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.710487" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.911736" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.163235" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.376987" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.967987" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="194.77" y="-1.01"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="198.9335" y="-1.01"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="205.185" y="-1.01"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="208.31075" y="-1.01"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="214.56226" y="-1.01"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-172.53999" y="36.610001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-164.188" y="36.610001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-160.02449" y="36.610001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-154.52318" y="36.610001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-147.74655" y="36.610001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-140.10722" y="36.610001"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-126.86" y="28.389999"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-117.44524" y="28.389999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-113.28174" y="28.389999"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-104.25458" y="28.389999"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-92.914352" y="28.389999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-82.849442" y="28.389999"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-76.597939" y="28.389999"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-67.170677" y="28.389999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-63.007179" y="28.389999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-53.454887" y="28.389999"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-42.114666" y="28.389999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-32.049751" y="28.389999"> )</gydF4y2Batspan> </text> <g> <path d="m 143.12,19.23 98.98,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,143.21,7.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.4147587" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.578258" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.643173" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.894672" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.309433" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.472931" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.037727" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.377945" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.030983" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="88.371201" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.622704" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.09" y="-8.75"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="115.25614" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="125.49609" y="-8.75"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="137.53648" y="-8.75"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="143.78798" y="-8.75"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="149.00174" y="-8.75"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="155.25323" y="-8.75"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="160.46698" y="-8.75"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="175.04549" y="-8.75"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="321.54001" y="-8.4899998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="325.70349" y="-8.4899998"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="331.95499" y="-8.4899998"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="335.08075" y="-8.4899998"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="341.33224" y="-8.4899998"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>当<年代pan class="equation" id="EEq7"> <svg height="34.674999" id="M43" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 34.674999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,34.675)"> <g transform="translate(72,-44.26)"> <text transform="matrix(1,0,0,-1,113.7,55.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> ⟶</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.395512" y="0"> ∞</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.973289" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.139431" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.503937" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.667435" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.168755" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.945381" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="92.584717" y="0"> ∼</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="105.82" y="-8.2200003"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="115.23476" y="-8.2200003"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="119.39825" y="-8.2200003"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="128.43793" y="-8.2200003"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="139.77815" y="-8.2200003"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="149.84306" y="-8.2200003"> )</gydF4y2Batspan> </text> <g> <path d="m 219.52,58.4 48.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,229.71,46.52)"> <tspan style="font-size: 12.50px; " x="41.279999" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.4147587" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.578258" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.643173" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.77,60.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="11.29008" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="17.2852" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,299.93,55.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="164.82001" y="0.25999999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="168.98351" y="0.25999999"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="175.235" y="0.25999999"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="178.36075" y="0.25999999"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="184.61224" y="0.25999999"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>对模型(<gydF4y2Baa href="#EEq2">2.1</gydF4y2Baa>),谱密度函数如下:<年代pan class="equation" id="EEq8"> <svg height="36.462502" id="M44" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 36.462502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,36.4625)"> <g transform="translate(72,-42.83)"> <text transform="matrix(1,0,0,-1,99.04,51.8)"> <tspan style="font-size: 12.50px; " x="44.889999" y="-9.2299995"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.678522" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.193066" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.832397" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,151.27,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </gydF4y2Batspan> </text> <g> <path d="m 143.11,54.92 13.86,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,143.11,43.04)"> <tspan style="font-size: 12.50px; " x="15.05" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.889999" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.790001" y="-8.7600002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.116999" y="-8.7600002"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.980663" y="-8.7600002"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.456497" y="-8.7600002"> n</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.439999" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.941319" y="-16.01"> </gydF4y2Batspan> </text> <g> <path d="m 199.55,54.92 14.02,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,203.44,43.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.33" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.931824" y="-3.8399999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,228.11,63.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,246.02,51.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.166139" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.893473" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.933861" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.911736" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.952126" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.553947" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="218.73" y="-2.49"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="222.89349" y="-2.49"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="229.145" y="-2.49"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="232.27075" y="-2.49"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="238.52225" y="-2.49"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>请注意,在频率谱密度函数是无限的<年代vg height="10.9125" id="M45" style="vertical-align:-0.17555pt;width:36.512501px;" version="1.1" viewbox="0 0 36.512501 10.9125" width="36.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.840821" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.117327" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.593161" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="13.125" id="M46" style="vertical-align:-1.95624pt;width:95.875px;" version="1.1" viewbox="0 0 95.875 13.125" width="95.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7398367" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.780226" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.031727" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.245476" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.823975" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.037727" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.201225" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.702545" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.178375" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.429878" y="0"> ]</gydF4y2Batspan> </text> </g> </g> </svg>。</pgydF4y2Ba> <p>当<年代vg height="9.875" id="M47" style="vertical-align:-2.29482pt;width:7.7624998px;" version="1.1" viewbox="0 0 7.7624998 9.875" width="7.7624998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="9.875" id="M48" style="vertical-align:-2.29482pt;width:7.9124999px;" version="1.1" viewbox="0 0 7.9124999 9.875" width="7.9124999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="10.75" id="M49" style="vertical-align:-0.15048pt;width:9.375px;" version="1.1" viewbox="0 0 9.375 10.75" width="9.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.75)"> <g transform="translate(72,-63.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="10.325" id="M50" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="10.325" id="M51" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="12.925" id="M52" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在模型(不同于零<gydF4y2Baa href="#EEq1">1.1</gydF4y2Baa>自协方差),关闭形式不能确定。然而,一些方法,比如贝尔泰利和Caporin提出的分割方法<gydF4y2Baa href="#B5">27</gydF4y2Baa>),用来计算自协方差的ARFIMA模型,还可以用于那些SARFIMA模型。</pgydF4y2Ba> <p>让<年代vg height="14.6" id="M53" style="vertical-align:-3.13504pt;width:29.0375px;" version="1.1" viewbox="0 0 29.0375 14.6" width="29.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.72,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.739357" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>表示SARFIMA的自协方差函数<年代vg height="14.7125" id="M54" style="vertical-align:-3.2316pt;width:109.375px;" version="1.1" viewbox="0 0 109.375 14.7125" width="109.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.277466" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.478714" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.13031" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.344061" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.070435" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.233932" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.397434" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.824215" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.025463" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.902832" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.116585" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.881424" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,11.1,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型。自协方差计算的分裂方法如下:<年代pan class="equation" id="eq2"> <svg height="48.412498" id="M55" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.412498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.4125)"> <g transform="translate(72,-33.27)"> <text transform="matrix(1,0,0,-1,130.8,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,137.15,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,144.11,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.940125" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,180.24,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,178.27,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,174.72,35.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.0499039" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="11.045024" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="17.040144" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,200.06,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,206.41,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,213.37,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ℎ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.37773" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.616728" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,237.35,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,244.3,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.715791" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.056011" y="0"> ℎ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.270245" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.521744" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="220.45" y="0.0099999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="224.61349" y="0.0099999998"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="230.86501" y="0.0099999998"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="233.99075" y="0.0099999998"> 8</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="240.24225" y="0.0099999998"> )</gydF4y2Batspan> </text> </g> </g> </svg></span> <svg height="14.6" id="M56" style="vertical-align:-3.13504pt;width:29.0375px;" version="1.1" viewbox="0 0 29.0375 14.6" width="29.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.72,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.739357" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="14.75" id="M57" style="vertical-align:-3.25793pt;width:29.0375px;" version="1.1" viewbox="0 0 29.0375 14.75" width="29.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.72,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.739357" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>自协方差函数SARFIMA吗<年代vg height="14.7125" id="M58" style="vertical-align:-3.2316pt;width:104.35px;" version="1.1" viewbox="0 0 104.35 14.7125" width="104.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.277466" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.478714" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.730213" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.943966" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.670338" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.833839" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.997337" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.424118" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.625366" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.876865" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.090614" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.855461" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,7.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和SARFIMA<年代vg height="14.7125" id="M59" style="vertical-align:-3.2316pt;width:104.35px;" version="1.1" viewbox="0 0 104.35 14.7125" width="104.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.481594" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.733093" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.896591" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.060093" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.311592" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.51284" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.390209" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.603958" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.855461" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,7.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型,分别。<年代vg height="14.75" id="M60" style="vertical-align:-3.25793pt;width:29.0375px;" version="1.1" viewbox="0 0 29.0375 14.75" width="29.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.72,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.739357" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>计算使用分割方法中给出以下表达式:<年代pan class="equation" id="eq3"> <svg height="48.412498" id="M61" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.412498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.4125)"> <g transform="translate(72,-33.27)"> <text transform="matrix(1,0,0,-1,130.8,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,137.15,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,144.11,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.940125" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,180.24,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,178.27,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,174.72,35.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.0499039" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="11.045024" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="17.040144" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,200.06,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,206.41,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,213.37,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ℎ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.37773" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.616728" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,237.35,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,244.3,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.715791" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.056011" y="0"> ℎ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.270245" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.521744" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="220.45" y="0.17"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="224.61349" y="0.17"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="230.86501" y="0.17"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="233.99075" y="0.17"> 9</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="240.24225" y="0.17"> )</gydF4y2Batspan> </text> </g> </g> </svg></span> <svg height="14.6" id="M62" style="vertical-align:-3.13504pt;width:29.0375px;" version="1.1" viewbox="0 0 29.0375 14.6" width="29.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.72,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.739357" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="14.75" id="M63" style="vertical-align:-3.25793pt;width:29.0375px;" version="1.1" viewbox="0 0 29.0375 14.75" width="29.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.72,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.739357" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>自协方差函数SARFIMA吗<年代vg height="14.7125" id="M64" style="vertical-align:-3.2316pt;width:103.85px;" version="1.1" viewbox="0 0 103.85 14.7125" width="103.85" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.867746" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.081497" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.332996" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.496498" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.659996" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.911495" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.112743" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.990112" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.203865" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.455368" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,6.68,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和SARFIMA<年代vg height="14.7125" id="M65" style="vertical-align:-3.2316pt;width:116.7625px;" version="1.1" viewbox="0 0 116.7625 14.7125" width="116.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.481594" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.733093" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.67226" y="0"> ×</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.449844" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.613342" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.864845" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="67.078598" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.330093" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.543846" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.795349" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,17.01,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型,分别。封闭的形式<年代vg height="14.6" id="M66" style="vertical-align:-3.13504pt;width:29.0375px;" version="1.1" viewbox="0 0 29.0375 14.6" width="29.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.72,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.739357" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在(<gydF4y2Baa href="#EEq5">2.4</gydF4y2Baa>)。自协方差的<年代vg height="14.75" id="M67" style="vertical-align:-3.25793pt;width:29.0375px;" version="1.1" viewbox="0 0 29.0375 14.75" width="29.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.72,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.739357" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>略微集成过程的自协方差和封闭的形式是由(<gydF4y2Baa href="#B4">28</gydF4y2Baa>)如下:<年代pan class="equation" id="EEq9"> <svg height="37.875" id="M68" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 37.875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,37.875)"> <g transform="translate(72,-41.7)"> <text transform="matrix(1,0,0,-1,110.46,52.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,116.81,49.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,123.77,52.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.940125" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.82" y="-8.2200003"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.983498" y="-8.2200003"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.548058" y="-8.2200003"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.799553" y="-8.2200003"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,205.73,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,210.97,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.4147587" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.578258" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.617928" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.958149" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.209648" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.611423" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 155.58,55.83 134.18,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,155.58,43.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="135.37" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.4200001" y="-0.0099999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.583499" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.135792" y="-0.0099999998"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.476013" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.903275" y="-0.0099999998"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.243496" y="-0.0099999998"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.494995" y="-0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="67.746498" y="-0.0099999998"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.173759" y="-0.0099999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="81.337257" y="-0.0099999998"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="90.364426" y="-0.0099999998"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="101.70464" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="111.25694" y="-0.0099999998"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="122.60966" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="130.01143" y="-0.0099999998"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,298.29,57.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,303.17,52.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="155.32001" y="-1.01"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="159.48351" y="-1.01"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="165.735" y="-1.01"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="168.86075" y="-1.01"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="175.11224" y="-1.01"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="181.36375" y="-1.01"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>生成系列,适合SARFIMA<年代vg height="14.7125" id="M69" style="vertical-align:-3.2316pt;width:62.825001px;" version="1.1" viewbox="0 0 62.825001 14.7125" width="62.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.6689" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.88265" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.647491" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.13,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型,下面的算法。</pgydF4y2Ba> <p><span class="statement" id="step1"><span class="statement-title"><i class="statement-title">步骤1。</我></span>生成<年代vg height="17.725" id="M70" style="vertical-align:-3.20526pt;width:107.75px;" version="1.1" viewbox="0 0 107.75 17.725" width="107.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.725)"> <g transform="translate(72,-57.82)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.843222" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.00672" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-37.7,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32.82,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-1.58,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,3.27,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,7.43,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>随机变量向量与标准正态分布。</年代pan></p> <p><span class="statement" id="step2"><span class="statement-title"><i class="statement-title">步骤2。</我></span>获取矩阵<年代vg height="14.6875" id="M71" style="vertical-align:-3.20526pt;width:93.3125px;" version="1.1" viewbox="0 0 93.3125 14.6875" width="93.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.64,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.31,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.54291" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.706408" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.370506" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.710728" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.574394" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.737892" y="0"> ]</gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="13.6125" id="M72" style="vertical-align:-2.34499pt;width:83.800003px;" version="1.1" viewbox="0 0 83.800003 13.6125" width="83.800003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.888433" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.0896807" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.429182" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.46957" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.721069" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.922318" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.513321" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.72707" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>利用表达式(<gydF4y2Baa href="#EEq5">2.4</gydF4y2Baa>)。</年代pan></p> <p><span class="statement" id="step3"><span class="statement-title"><i class="statement-title">步骤3。</我></span>将协方差矩阵如下:<年代vg height="13.725" id="M73" style="vertical-align:-0.0pt;width:59.150002px;" version="1.1" viewbox="0 0 59.150002 13.725" width="59.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.777826" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.818214" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.157715" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-31.45,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在那里,<年代vg height="10.6875" id="M74" style="vertical-align:-0.0pt;width:10.55px;" version="1.1" viewbox="0 0 10.55 10.6875" width="10.55" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个下三角矩阵。</年代pan></p> <p>这种分裂称为柯列斯基。可以获得柯列斯基分解的正定对称矩阵。请注意,矩阵<年代vg height="14.6875" id="M75" style="vertical-align:-3.20526pt;width:16.575001px;" version="1.1" viewbox="0 0 16.575001 14.6875" width="16.575001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.64,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>正定对称。</pgydF4y2Ba> <p><span class="statement" id="step4"><span class="statement-title"><i class="statement-title">步骤4。</我></span>获得系列<年代vg height="17.725" id="M76" style="vertical-align:-3.20526pt;width:117.7px;" version="1.1" viewbox="0 0 117.7 17.725" width="117.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.725)"> <g transform="translate(72,-57.82)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-33.37,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-28.5,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,6.39,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,11.23,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,15.4,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>通过使用<年代vg height="17.725" id="M77" style="vertical-align:-3.20526pt;width:157.9375px;" version="1.1" viewbox="0 0 157.9375 17.725" width="157.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.725)"> <g transform="translate(72,-57.82)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-33.37,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-28.5,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,6.39,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,11.23,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,15.4,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,25.58,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.37989" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>公式。<年代vg height="14.6875" id="M78" style="vertical-align:-3.20526pt;width:109.3125px;" version="1.1" viewbox="0 0 109.3125 14.6875" width="109.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-33.37,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-28.5,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,6.39,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,11.23,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>有一个合适的结构SARFIMA吗<年代vg height="14.7125" id="M79" style="vertical-align:-3.2316pt;width:56.974998px;" version="1.1" viewbox="0 0 56.974998 14.7125" width="56.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型。</年代pan></p> <p><span class="statement" id="step5"><span class="statement-title"><i class="statement-title">第5步。</我></span>根据SARMA生成系列<年代vg height="14.7125" id="M80" style="vertical-align:-3.2316pt;width:43.974998px;" version="1.1" viewbox="0 0 43.974998 14.7125" width="43.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.556372" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-41.22,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型通过<年代vg height="14.6875" id="M81" style="vertical-align:-3.20526pt;width:109.3125px;" version="1.1" viewbox="0 0 109.3125 14.6875" width="109.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-33.37,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-28.5,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,6.39,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,11.23,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>错误系列。通过这种方式,新生成的系列SARFIMA的结构<年代vg height="14.7125" id="M82" style="vertical-align:-3.2316pt;width:62.825001px;" version="1.1" viewbox="0 0 62.825001 14.7125" width="62.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.6689" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.88265" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.647491" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.13,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。这个算法很容易扩展到SARFIMA<年代vg height="14.7125" id="M83" style="vertical-align:-3.2316pt;width:109.375px;" version="1.1" viewbox="0 0 109.375 14.7125" width="109.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.277466" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.478714" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.13031" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.344061" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.070435" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.233932" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.397434" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.824215" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.025463" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.902832" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.116585" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.881424" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,11.1,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型。</年代pan></p> <h4 id="the-two-staged-method">3所示。两步方法</gydF4y2Bah4> <p>两阶段方法可以用来估计SARFIMA的参数<年代vg height="14.7125" id="M84" style="vertical-align:-3.2316pt;width:62.825001px;" version="1.1" viewbox="0 0 62.825001 14.7125" width="62.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.6689" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.88265" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.647491" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.13,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型。在第一阶段的这种方法,它假定时间序列有一个合适的结构使用SARFIMA<年代vg height="14.7125" id="M85" style="vertical-align:-3.2316pt;width:56.974998px;" version="1.1" viewbox="0 0 56.974998 14.7125" width="56.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>参数模型和季节性略微不同<年代vg height="10.325" id="M86" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>估计。在第二个阶段,参数的估计,EML下面给出的方法,可以使用。</pgydF4y2Ba> <p>SARFIMA理论自协方差和自相关函数<年代vg height="14.7125" id="M87" style="vertical-align:-3.2316pt;width:56.974998px;" version="1.1" viewbox="0 0 56.974998 14.7125" width="56.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型所示(<gydF4y2Baa href="#EEq5">2.4</gydF4y2Baa>)和(<gydF4y2Baa href="#EEq5">2.5</gydF4y2Baa>分别)。让时间序列<年代vg height="14.3375" id="M88" style="vertical-align:-3.21404pt;width:16.512501px;" version="1.1" viewbox="0 0 16.512501 14.3375" width="16.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>有<年代vg height="7.1374998" id="M89" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>观察<年代vg height="14.6875" id="M90" style="vertical-align:-3.20526pt;width:71.137497px;" version="1.1" viewbox="0 0 71.137497 14.6875" width="71.137497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-24.15,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-19.3,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,让<年代vg height="10.6875" id="M91" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>代表的自相关矩阵<年代vg height="11.0125" id="M92" style="vertical-align:-3.20526pt;width:60.724998px;" version="1.1" viewbox="0 0 60.724998 11.0125" width="60.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.2,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-28.32,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。因此,的似然函数<年代vg height="11.0125" id="M93" style="vertical-align:-3.20526pt;width:60.724998px;" version="1.1" viewbox="0 0 60.724998 11.0125" width="60.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.2,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-28.32,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>如下:<年代pan class="equation" id="EEq10"> <svg height="30.700001" id="M94" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.700001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7)"> <g transform="translate(72,-47.44)"> <text transform="matrix(1,0,0,-1,96.45,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.927622" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.091121" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.156036" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.795368" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.835758" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.999256" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.250755" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.852581" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,163.47,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.77792" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,181.12,57.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.58"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.23" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.23" y="3.1600001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,195.85,63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.804176" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,215.61,56.25)"> <tspan style="font-size: 12.50px; " x="22.219999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.190001" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.950001" y="-7.25"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> p</gydF4y2Batspan> </text> <g> <path d="m 256.56,59.37 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,256.56,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.4400001" y="-8.7600002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,273.03,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,276.51,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,286.23,61.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,297.1,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.0299997" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.08" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="167.64999" y="-0.34999999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="171.81349" y="-0.34999999"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="178.065" y="-0.34999999"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="181.19075" y="-0.34999999"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="187.44225" y="-0.34999999"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>柯列斯基分解用于矩阵<年代vg height="10.6875" id="M95" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>上下三角矩阵的乘法计算似然函数。而不是计算矩阵的逆<年代vg height="10.6875" id="M96" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>(<年代vg height="8.7875004" id="M97" style="vertical-align:-0.3135pt;width:32.612499px;" version="1.1" viewbox="0 0 32.612499 8.7875004" width="32.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.7875)"> <g transform="translate(72,-64.97)"> <text transform="matrix(1,0,0,-1,-71.95,65.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.9896574" y="0"> ×</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.767242" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>),较低的逆和上三角矩阵计算通过使用分解。因此,分解降低计算难度和计算时间。柯列斯基分解的矩阵<年代vg height="10.6875" id="M98" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>写如下:<年代pan class="equation" id="eq4"> <svg height="17.4625" id="M99" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 17.4625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.4625)"> <g transform="translate(72,-58.03)"> <text transform="matrix(1,0,0,-1,184.12,61.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.231054" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.570557" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,226.03,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,229.51,61.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="235.24001" y="-0.050000001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="239.4035" y="-0.050000001"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="245.655" y="-0.050000001"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="248.78075" y="-0.050000001"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="255.03224" y="-0.050000001"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>让<年代vg height="14.2125" id="M100" style="vertical-align:-0.1881pt;width:70.4375px;" version="1.1" viewbox="0 0 70.4375 14.2125" width="70.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2125)"> <g transform="translate(72,-60.63)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.00672" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.6,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-24.73,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,它可以写<年代pan class="equation" id="eq5"> <svg height="54.525002" id="M101" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 54.525002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,54.525)"> <g transform="translate(72,-28.38)"> <text transform="matrix(1,0,0,-1,76,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,85.03,63.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,88.51,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,98.23,63.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,109.1,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,142.67,63.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,146.14,55.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.189501" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,168.67,63.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,172.15,55.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,178,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.87,58.5)"> <tspan style="font-size: 12.50px; " x="24.530001" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.389999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,227.6,63.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.46,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.0299997" y="2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,253.34,66.3)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,258.9,55.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,273.09,63.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,283.96,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.0299997" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.35" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.390388" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,326.85,63.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,330.33,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-187.71001" y="24.690001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-187.71001" y="27.85"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-185.21001" y="26.280001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-175.48" y="24.690001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-175.48" y="27.85"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,157.35,38.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.804176" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,178.5,32.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="1.5700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.54" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.879501" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,209.72,37.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,213.19,33.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,215.69,39.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.804176" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,236.84,32.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="1.5700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.54" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.879999" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.879999" y="1.5700001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,262.22,38.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,273.09,32.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="191.66" y="-14.85"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="195.8235" y="-14.85"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="202.075" y="-14.85"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="205.20074" y="-14.85"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="211.45226" y="-14.85"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>因此,(<gydF4y2Baa href="#EEq10">3.1</gydF4y2Baa>)可以写成<年代pan class="equation" id="EEq11"> <svg height="30.700001" id="M102" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.700001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7)"> <g transform="translate(72,-47.44)"> <text transform="matrix(1,0,0,-1,92.56,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.39" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.950001" y="-7.25"> </gydF4y2Batspan> </text> <g> <path d="m 112.51,59.37 10.06,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,113.02,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.75" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.82" y="-8.7600002"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.847885" y="-8.7600002"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.39922" y="-8.7600002"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.650719" y="-8.7600002"> p</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.990219" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.153717" y="-8.7600002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.40522" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.007042" y="-8.7600002"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,189.2,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.77792" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,206.85,57.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.58"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.84" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.84" y="3.1600001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,220.19,63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,233.14,56.25)"> <tspan style="font-size: 12.50px; " x="22.23" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.190001" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.950001" y="-7.25"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> p</gydF4y2Batspan> </text> <g> <path d="m 274.09,59.37 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,274.09,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.7600002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,294.04,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,297.51,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.51" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.559999" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="167.24001" y="-0.34999999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="171.4035" y="-0.34999999"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="177.655" y="-0.34999999"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="180.78075" y="-0.34999999"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="187.03224" y="-0.34999999"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>的似然函数(<gydF4y2Baa href="#EEq11">3.4</gydF4y2Baa>)是最大化的季节性略微不同参数通过使用一个优化算法。季节性后略微不同参数估计通过使用EML, SARMA的其他参数<年代vg height="14.7125" id="M103" style="vertical-align:-3.2316pt;width:43.974998px;" version="1.1" viewbox="0 0 43.974998 14.7125" width="43.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.556372" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-41.22,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型估计在第二阶段通过使用经典的方法。在第二个阶段,季节性的顺序模型可以由使用Box-Jenkins方法决定的。因此,两步方法可以概括如下。</pgydF4y2Ba> <p><span class="statement" id="phase1"><span class="statement-title"><i class="statement-title">阶段1。</我></span>估计参数<年代vg height="10.325" id="M104" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>通过假设适合SARFIMA时间序列<年代vg height="14.7125" id="M105" style="vertical-align:-3.2316pt;width:56.974998px;" version="1.1" viewbox="0 0 56.974998 14.7125" width="56.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。</年代pan></p> <p><span class="statement" id="phase2"><span class="statement-title"><i class="statement-title">阶段2。</我></span>估计季节性自回归和移动平均参数通过Box-Jenkins方法。</年代pan></p> <h4 id="the-css-method">4所示。CSS的方法</gydF4y2Bah4> <p>钟,柏丽<gydF4y2Baa href="#B8">20.</gydF4y2Baa>)提出了一个基于最小化方法的条件和广场。这种方法可以用于SARFIMA<年代vg height="14.7125" id="M106" style="vertical-align:-3.2316pt;width:109.375px;" version="1.1" viewbox="0 0 109.375 14.7125" width="109.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.277466" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.478714" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.13031" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.344061" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.070435" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.233932" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.397434" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.824215" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.025463" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.902832" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.116585" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.881424" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,11.1,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型。条件的总和广场SARFIMA模型方法如下:<年代pan class="equation" id="EEq12"> <svg height="48.325001" id="M107" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.325001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.325)"> <g transform="translate(72,-33.34)"> <text transform="matrix(1,0,0,-1,-10.64,49.67)"> <tspan style="font-size: 12.50px; " x="23.639999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.200001" y="-7.2600002"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> =</gydF4y2Batspan> </text> <g> <path d="m 21.56,52.8 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,21.56,40.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-3.8299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.279999" y="-6.2399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.130001" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.129999" y="-8.75"> l</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.605833" y="-8.75"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.857334" y="-8.75"> g</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,72.03,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,76.9,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.98" y="4.8099999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.66" y="-9.7700005"> 1</gydF4y2Batspan> </text> <g> <path d="m 107.45,52.8 18.46,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,107.45,39.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,121.04,43.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="7.1599998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,127.11,42.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,144.47,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,138.57,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,140.09,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7393761" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7344961" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,156.81,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.1900001" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,170.55,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,183.5,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.365707" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.604704" y="0"> Θ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,212.14,54.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,225.1,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.353204" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.604704" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.757139" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.920639" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.122849" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.361843" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.989635" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.15313" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.355339" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="80.606842" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.77034" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.797508" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="105.13773" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="114.33994" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,343.61,54.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,349.29,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,383.03,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,387.38,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,391.54,55.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,399.09,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,408.96,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,412.2,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,419.39,57.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,424.26,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.490002" y="0.13"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.6535" y="0.13"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.904999" y="0.13"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.03075" y="0.13"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.282249" y="0.13"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>CSS的方法,首先,季节性略微不同程序执行<年代vg height="14.3375" id="M108" style="vertical-align:-3.21404pt;width:16.512501px;" version="1.1" viewbox="0 0 16.512501 14.3375" width="16.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。其次,略微不同程序执行<年代vg height="17.737499" id="M109" style="vertical-align:-3.21404pt;width:78.762497px;" version="1.1" viewbox="0 0 78.762497 17.737499" width="78.762497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.7375)"> <g transform="translate(72,-57.81)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-38.21,66.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-33.86,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-29.7,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-22.15,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.28,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。第三,SARMA过滤应用<年代vg height="17.9" id="M110" style="vertical-align:-3.21404pt;width:133.2375px;" version="1.1" viewbox="0 0 133.2375 17.9" width="133.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9)"> <g transform="translate(72,-57.68)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.733093" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.05,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-28.37,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,5.37,65.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,9.72,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,13.88,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,21.43,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,31.3,57.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。通过计算获得的这个系列的平方和<年代vg height="17.987499" id="M111" style="vertical-align:-3.21404pt;width:297.45001px;" version="1.1" viewbox="0 0 297.45001 17.987499" width="297.45001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9875)"> <g transform="translate(72,-57.61)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.23,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-50.37,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.865587" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.029085" y="0"> Θ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-24.31,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.44,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.865587" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.029085" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.093521" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.257021" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.959106" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.122608" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.662395" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.825893" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.527985" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.691483" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.85498" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="81.882149" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.222366" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="102.42458" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,93.15,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,98.83,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,132.57,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,136.92,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,141.09,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,148.63,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,158.51,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,161.74,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>的平方计算条件和一个固定的值<年代vg height="17.799999" id="M112" style="vertical-align:-3.2316pt;width:15.3875px;" version="1.1" viewbox="0 0 15.3875 17.799999" width="15.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8)"> <g transform="translate(72,-57.76)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="10.325" id="M113" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。钟,柏丽<gydF4y2Baa href="#B8">20.</gydF4y2Baa>)也强调,CSS的方法获得的参数的估计偏差的平均值少了系列。很容易使用CSS的方法,因为它不需要计算自协方差。在文献中,CSS SARFIMA方法<年代vg height="14.7125" id="M114" style="vertical-align:-3.2316pt;width:62.825001px;" version="1.1" viewbox="0 0 62.825001 14.7125" width="62.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.6689" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.88265" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.647491" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.13,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型已经被Darne只用et al。<gydF4y2Baa href="#B10">19</gydF4y2Baa>]。</pgydF4y2Ba> <h4 id="simulation-study">5。模拟研究</gydF4y2Bah4> <p>在本节中,SARFIMA的参数<年代vg height="14.7125" id="M115" style="vertical-align:-3.2316pt;width:62.825001px;" version="1.1" viewbox="0 0 62.825001 14.7125" width="62.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.6689" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.88265" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.647491" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.13,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型估计通过使用CSS和两步方法分别在不同参数设置和样本大小。此外,这两种方法的优点和缺点进行了讨论。</pgydF4y2Ba> <p>给出了部分算法的步骤<gydF4y2Baa href="#sec2">2</gydF4y2Baa>,用于生成各种SARFIMA<年代vg height="14.7125" id="M116" style="vertical-align:-3.2316pt;width:62.825001px;" version="1.1" viewbox="0 0 62.825001 14.7125" width="62.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.6689" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.88265" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.647491" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.13,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型。SARFIMA<年代vg height="14.7125" id="M117" style="vertical-align:-3.2316pt;width:56.974998px;" version="1.1" viewbox="0 0 56.974998 14.7125" width="56.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和SARFIMA<年代vg height="14.7125" id="M118" style="vertical-align:-3.2316pt;width:56.974998px;" version="1.1" viewbox="0 0 56.974998 14.7125" width="56.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>强调模型的仿真研究。对于SARFIMA<年代vg height="14.7125" id="M119" style="vertical-align:-3.2316pt;width:56.974998px;" version="1.1" viewbox="0 0 56.974998 14.7125" width="56.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型中,36个不同的情况下检查如季节性略微不同<年代vg height="12.8875" id="M120" style="vertical-align:-1.76814pt;width:103.4875px;" version="1.1" viewbox="0 0 103.4875 12.8875" width="103.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.009838" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.223591" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.47509" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.600842" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.852341" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="67.053589" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.305092" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.43084" y="0"> 3</gydF4y2Batspan> </text> </g> </g> </svg>、季节性自回归参数<年代vg height="13.45" id="M121" style="vertical-align:-2.21957pt;width:171.35001px;" version="1.1" viewbox="0 0 171.35001 13.45" width="171.35001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.00312" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.043509" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.29501" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.420757" y="0"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.67226" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.886009" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.137508" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.26326" y="0"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.514759" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.716011" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.879509" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="79.444061" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="85.695564" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="88.821312" y="0"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="95.072815" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="99.236313" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="104.45007" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="108.61356" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="117.17812" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="123.42962" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="126.55537" y="0"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="132.80687" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>、样本大小<年代vg height="13.0125" id="M122" style="vertical-align:-1.76814pt;width:110.6375px;" version="1.1" viewbox="0 0 110.6375 13.0125" width="110.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0125)"> <g transform="translate(72,-61.59)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.6773224" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.71771" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.969212" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.220711" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.47221" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.685963" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.937462" y="0"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.188961" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.44046" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.641708" y="0"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.893211" y="0"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.144707" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,期<年代vg height="10.8625" id="M123" style="vertical-align:-0.13794pt;width:34.200001px;" version="1.1" viewbox="0 0 34.200001 10.8625" width="34.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8625)"> <g transform="translate(72,-63.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.9646511" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.005039" y="0"> 4</gydF4y2Batspan> </text> </g> </g> </svg>。类似的,相同的参数也用于SARFIMA<年代vg height="14.7125" id="M124" style="vertical-align:-3.2316pt;width:56.974998px;" version="1.1" viewbox="0 0 56.974998 14.7125" width="56.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型通过<年代vg height="13.45" id="M125" style="vertical-align:-2.21957pt;width:170.71249px;" version="1.1" viewbox="0 0 170.71249 13.45" width="170.71249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.782387" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.159637" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.373386" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.624886" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.750637" y="0"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.002136" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.203384" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.366882" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.931442" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="85.182938" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="88.308685" y="0"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.560188" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="98.723686" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="103.93744" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="108.10094" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="116.66549" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="122.91699" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="126.04274" y="0"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="132.29425" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。对于每个案例,1000生成时间序列,所以完全我们生成72000时间序列。生成的时间序列的参数估计通过使用CSS和两步方法的结果在表中进行了总结<gydF4y2Baa href="//www.newsama.com/journals/jps/2011/691058/tab1/" target="_blank">1</gydF4y2Baa>和<gydF4y2Baa href="//www.newsama.com/journals/jps/2011/691058/tab2/" target="_blank">2</gydF4y2Baa>。每1000次系列、均值、标准差和均方根误差(RMSE)估计参数的值在这些表展出。RMSE值计算<年代pan class="equation" id="eq6"> <svg height="49.212502" id="M126" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 49.212502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,49.2125)"> <g transform="translate(72,-32.63)"> <text transform="matrix(1,0,0,-1,132.81,42.61)"> <tspan style="font-size: 12.50px; " x="49.560001" y="3.5599999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.508999" y="0"> =</gydF4y2Batspan> </text> <g> <path d="m 195.82,70.71 85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,197.01,53.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,208.44,59.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7519999" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.128" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="9.9399996"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="9.9399996"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7169924" y="9.9399996"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,228.53,50.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,241.36,50.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,247.36,53.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.700001" y="-2.73"> ̂</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.34" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,265.68,50.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,268.9,50.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,274.75,61.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <g> <path d="m 197.01,45.73 82.61,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,225.81,33.86)"> <tspan style="font-size: 12.50px; " x="55.009998" y="-8.75"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.503" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.754499" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="238.94" y="-15.33"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="243.1035" y="-15.33"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="249.355" y="-15.33"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="252.48074" y="-15.33"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="258.73224" y="-15.33"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.5875" id="M127" style="vertical-align:-3.2316pt;width:12.875px;" version="1.1" viewbox="0 0 12.875 14.5875" width="12.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.97,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="18.0875" id="M128" style="vertical-align:-3.2316pt;width:12.875px;" version="1.1" viewbox="0 0 12.875 18.0875" width="12.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.0875)"> <g transform="translate(72,-57.53)"> <text transform="matrix(1,0,0,-1,-65.59,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̂</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-6.3600001" y="2.72"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.97,57.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>分别表示真正的和估计的参数值。</pgydF4y2Ba> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jps/2011/691058/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 仿真结果SARFIMA CSS和两阶段的方法<年代vg height="14.6" id="M129" style="vertical-align:-3.13504pt;width:57.625px;" version="1.1" viewbox="0 0 57.625 14.6" width="57.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Badiv> <a class="table-thumb-overlay" href="//www.newsama.com/journals/jps/2011/691058/tab1" target="_blank" aria-label="View full page"></a> </div> </div> <div class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jps/2011/691058/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 在SARFIMA CSS和两阶段方法的仿真结果<年代vg height="14.6" id="M138" style="vertical-align:-3.13504pt;width:57.625px;" version="1.1" viewbox="0 0 57.625 14.6" width="57.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Badiv> <a class="table-thumb-overlay" href="//www.newsama.com/journals/jps/2011/691058/tab2" target="_blank" aria-label="View full page"></a> </div> </div> <p>在表<gydF4y2Baa href="//www.newsama.com/journals/jps/2011/691058/tab1/" target="_blank">1</gydF4y2Baa>,SARFIMA<年代vg height="14.7125" id="M147" style="vertical-align:-3.2316pt;width:56.974998px;" version="1.1" viewbox="0 0 56.974998 14.7125" width="56.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型,仿真结果为不同的值<年代vg height="10.475" id="M148" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>和样本容量<年代vg height="7.1374998" id="M149" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>显示当CSS和两阶段方法执行。从这个表中,CSS的方法,我们观察到RMSE值大幅降低季节性分数估计参数的差异和季节性自回归,当样本容量也在不断增加。也见过RMSE值不改变很多季节性自回归参数的符号是否积极。拥有更大的季节性自回归参数的绝对价值,RMSE值季节性自回归(<年代vg height="13.45" id="M150" style="vertical-align:-2.21957pt;width:65.012497px;" version="1.1" viewbox="0 0 65.012497 13.45" width="65.012497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>)参数变小。当<年代vg height="10.9125" id="M151" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="10.9125" id="M152" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>相比,的值<年代vg height="13.45" id="M153" style="vertical-align:-2.21957pt;width:65.4375px;" version="1.1" viewbox="0 0 65.4375 13.45" width="65.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.086536" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在<年代vg height="10.9125" id="M154" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>较小的比吗<年代vg height="10.9125" id="M155" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>,而的值<年代vg height="13.45" id="M156" style="vertical-align:-2.21957pt;width:65.012497px;" version="1.1" viewbox="0 0 65.012497 13.45" width="65.012497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在<年代vg height="10.9125" id="M157" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="10.9125" id="M158" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="10.9125" id="M159" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 3</gydF4y2Batspan> </text> </g> </g> </svg>彼此接近。注意,的值<年代vg height="13.45" id="M160" style="vertical-align:-2.21957pt;width:65.4375px;" version="1.1" viewbox="0 0 65.4375 13.45" width="65.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.086536" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在<年代vg height="10.9125" id="M161" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 3</gydF4y2Batspan> </text> </g> </g> </svg>更大比<年代vg height="10.9125" id="M162" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>。</pgydF4y2Ba> <p>根据表<gydF4y2Baa href="//www.newsama.com/journals/jps/2011/691058/tab1/" target="_blank">1</gydF4y2Baa>两步方法执行时,可以看出样本大小不影响显著的RMSE值,特别是对于<年代vg height="13.45" id="M163" style="vertical-align:-2.21957pt;width:65.012497px;" version="1.1" viewbox="0 0 65.012497 13.45" width="65.012497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>当<年代vg height="10.9125" id="M164" style="vertical-align:-0.17555pt;width:61.674999px;" version="1.1" viewbox="0 0 61.674999 10.9125" width="61.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.00312" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.043509" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.608063" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.859566" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.985313" y="0"> 7</gydF4y2Batspan> </text> </g> </g> </svg>。然而,当季节性自回归参数的估计绝对值增加,的值<年代vg height="13.45" id="M165" style="vertical-align:-2.21957pt;width:65.012497px;" version="1.1" viewbox="0 0 65.012497 13.45" width="65.012497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>显著增加<年代vg height="10.9125" id="M166" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="10.9125" id="M167" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>。的值<年代vg height="13.45" id="M168" style="vertical-align:-2.21957pt;width:65.4375px;" version="1.1" viewbox="0 0 65.4375 13.45" width="65.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.086536" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>不受季节性自回归参数的符号和大小,尤其是在吗<年代vg height="10.9125" id="M169" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>。值得指出的是,的值<年代vg height="13.45" id="M170" style="vertical-align:-2.21957pt;width:65.4375px;" version="1.1" viewbox="0 0 65.4375 13.45" width="65.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.086536" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>相当大的季节性自回归参数的负<年代vg height="10.9125" id="M171" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="10.9125" id="M172" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 3</gydF4y2Batspan> </text> </g> </g> </svg>。它可以推断出从对比<年代vg height="10.9125" id="M173" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="10.9125" id="M174" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>为负的季节性自回归参数,两者的值<年代vg height="13.45" id="M175" style="vertical-align:-2.21957pt;width:65.4375px;" version="1.1" viewbox="0 0 65.4375 13.45" width="65.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.086536" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="13.45" id="M176" style="vertical-align:-2.21957pt;width:65.012497px;" version="1.1" viewbox="0 0 65.012497 13.45" width="65.012497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>逐渐增加的同时<年代vg height="10.325" id="M177" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>正在增加。特别是,的值<年代vg height="13.45" id="M178" style="vertical-align:-2.21957pt;width:65.012497px;" version="1.1" viewbox="0 0 65.012497 13.45" width="65.012497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.748959" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在<年代vg height="10.9125" id="M179" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 3</gydF4y2Batspan> </text> </g> </g> </svg>得到最大的季节性自回归参数的值是负的。因此,对于季节性自回归参数的负值,我们可以说,估计误差变大,而季节性的不同部分是增加的顺序。</pgydF4y2Ba> <p>在表<gydF4y2Baa href="//www.newsama.com/journals/jps/2011/691058/tab2/" target="_blank">2</gydF4y2Baa>,SARFIMA<年代vg height="14.7125" id="M180" style="vertical-align:-3.2316pt;width:56.974998px;" version="1.1" viewbox="0 0 56.974998 14.7125" width="56.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>模型,仿真结果为不同值的参数<年代vg height="10.9125" id="M181" style="vertical-align:-0.17555pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.9125" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</gydF4y2Batspan> </text> </g> </g> </svg>和样本容量<年代vg height="7.1374998" id="M182" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>所示的CSS和两步方法。从这个表中,我们观察到RMSE值减少了季节性的分数估计参数的差异和季节性移动平均,当样本容量增加,CSS的方法执行。也见过RMSE值不改变参数的符号是否季节性移动平均线是积极的。在有季节性移动平均参数的较大值为负值,季节性的RMSE值略微差异(<年代vg height="13.45" id="M183" style="vertical-align:-2.21957pt;width:65.4375px;" version="1.1" viewbox="0 0 65.4375 13.45" width="65.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.086536" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>)小。当我们比较<年代vg height="10.9125" id="M184" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>与<年代vg height="10.9125" id="M185" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>的值,<年代vg height="13.45" id="M186" style="vertical-align:-2.21957pt;width:65.4375px;" version="1.1" viewbox="0 0 65.4375 13.45" width="65.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.086536" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在<年代vg height="10.9125" id="M187" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>较小的比吗<年代vg height="10.9125" id="M188" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>,而的值<年代vg height="13.45" id="M189" style="vertical-align:-2.21957pt;width:64.375px;" version="1.1" viewbox="0 0 64.375 13.45" width="64.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> Θ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.236336" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在<年代vg height="10.9125" id="M190" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="10.9125" id="M191" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>,<年代vg height="10.9125" id="M192" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 3</gydF4y2Batspan> </text> </g> </g> </svg>彼此接近。注意,的值<年代vg height="13.45" id="M193" style="vertical-align:-2.21957pt;width:65.4375px;" version="1.1" viewbox="0 0 65.4375 13.45" width="65.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.086536" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在<年代vg height="10.9125" id="M194" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 3</gydF4y2Batspan> </text> </g> </g> </svg>更大比<年代vg height="10.9125" id="M195" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>。</pgydF4y2Ba> <p>当表<gydF4y2Baa href="//www.newsama.com/journals/jps/2011/691058/tab2/" target="_blank">2</gydF4y2Baa>检查,观察到的值<年代vg height="13.45" id="M196" style="vertical-align:-2.21957pt;width:64.375px;" version="1.1" viewbox="0 0 64.375 13.45" width="64.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> Θ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.236336" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>减少为两步方法当样本容量增加。然而,并没有积极的还是消极的季节性移动平均参数的值之间的关系和的值<年代vg height="13.45" id="M197" style="vertical-align:-2.21957pt;width:65.4375px;" version="1.1" viewbox="0 0 65.4375 13.45" width="65.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.086536" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>和<年代vg height="13.45" id="M198" style="vertical-align:-2.21957pt;width:64.375px;" version="1.1" viewbox="0 0 64.375 13.45" width="64.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> Θ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.236336" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>当执行两阶段方法。我们想要的话<年代vg height="13.45" id="M199" style="vertical-align:-2.21957pt;width:64.375px;" version="1.1" viewbox="0 0 64.375 13.45" width="64.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> Θ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.236336" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>每个样本大小的最小值<年代vg height="10.9125" id="M200" style="vertical-align:-0.17555pt;width:50.337502px;" version="1.1" viewbox="0 0 50.337502 10.9125" width="50.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.782387" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 7</gydF4y2Batspan> </text> </g> </g> </svg>这值<年代vg height="13.45" id="M201" style="vertical-align:-2.21957pt;width:65.4375px;" version="1.1" viewbox="0 0 65.4375 13.45" width="65.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.406336" y="0"> E</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.086536" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>相当大的负的季节性移动平均线参数对其积极的价值观<年代vg height="10.9125" id="M202" style="vertical-align:-0.17555pt;width:51.400002px;" version="1.1" viewbox="0 0 51.400002 10.9125" width="51.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.632589" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.758339" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>,在表0.3<gydF4y2Baa href="//www.newsama.com/journals/jps/2011/691058/tab2/" target="_blank">2</gydF4y2Baa>。</pgydF4y2Ba> <h4 id="discussions">6。讨论</gydF4y2Bah4> <p>在文献中,两步方法是一种广泛使用SARFIMA模型的方法来估计参数。虽然还有另一个名为CSS的方法,这种方法没有被用来估计SARFIMA模型的参数。在这项研究中,CSS和SARFIMA的两步方法用来估计参数模型进行仿真研究,并通过这种方式这两个方法的属性检查下不同的参数设置和样本大小。</pgydF4y2Ba> <p>从模拟的结果,我们推断,当样本容量增加,CSS的方法给出了更精确的估计。除此之外,我们可以推断在SARFIMA当季节性自回归参数<年代vg height="14.6" id="M203" style="vertical-align:-3.13504pt;width:57.625px;" version="1.1" viewbox="0 0 57.625 14.6" width="57.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> </g> </g> </svg>模型接近1或−1,CSS的参数估计方法有更少的错误。CSS的方法产生很好的估计<年代vg height="10.325" id="M204" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>当在SARFIMA季节性自回归参数<年代vg height="14.6" id="M205" style="vertical-align:-3.13504pt;width:57.625px;" version="1.1" viewbox="0 0 57.625 14.6" width="57.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> </g> </g> </svg>模型和季节性移动平均线在SARFIMA参数<年代vg height="14.6" id="M206" style="vertical-align:-3.13504pt;width:57.625px;" version="1.1" viewbox="0 0 57.625 14.6" width="57.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.493616" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.82,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> </g> </g> </svg>模型是积极的。</pgydF4y2Ba> <p>当CSS的方法是与两步方法相比,CSS方法RMSE值低于两步方法在不同参数设置和样本大小,尤其是自回归模型。两步方法产生误导的结果<年代vg height="10.475" id="M207" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>选择附近−1<年代vg height="13.45" id="M208" style="vertical-align:-2.21957pt;width:72.087502px;" version="1.1" viewbox="0 0 72.087502 13.45" width="72.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.166618" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.207008" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.771564" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.023064" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.148811" y="0"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.400314" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。然而,这并非如此的CSS的方法。基于结果和简单的方法,即将研究它可以很容易地显示CSS的方法应该首选而不是两步SARFIMA模型的参数估计方法。</pgydF4y2Ba> </div> </div> <div class="ArticleReferences_xmlContent__p_40j"> <h4 class="ArticleReferences_references__GH2t_" id="references">引用</gydF4y2Bah4> <ol class="ArticleReferences_orderedReferences__mJr9M"> <li class="ArticleReferences_articleReference__ouEuh" id="B3"> <div class="referenceContent"> <p class="referenceText">r·t·柏丽“长记忆过程和部分集成在计量经济学,”<我>计量经济学杂志</我>,卷73,不。1,5-59,1996页。</pgydF4y2Ba>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1016/0304-4076(95)01732-1" target="_blank" rel="noreferrer">出版商的网站</gydF4y2Baa> <span class="sep">|</年代pan> <a href="https://scholar.google.com/scholar_lookup?title=Long%20memory%20processes%20and%20fractional%20integration%20in%20econometrics&author=R.%20T.%20Baillie&publication_year=1996" target="_blank" rel="noreferrer">谷歌学术搜索</gydF4y2Baa> <span class="sep">|</年代pan> <a 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14"> <defs> <clippath id="a"> <path d="M10.293,13.707a1,1,0,0,1,0-1.414L14.586,8H1A1,1,0,0,1,1,6H14.586L10.293,1.707A1,1,0,0,1,11.707.293l6,6a1,1,0,0,1,.172.231h0l.01.019,0,.005.007.014.006.012,0,.008.008.018v0a1,1,0,0,1-.009.817l0,0L17.9,7.44l0,.009-.005.011-.007.013,0,.008-.008.015,0,.005-.01.016,0,0-.011.017,0,0-.012.018,0,0-.012.017,0,0L17.8,7.6l0,0-.011.014,0,.006-.01.012-.009.011-.006.007-.015.017h0l-.04.042-6,6a1,1,0,0,1-1.414,0Z" transform="translate(3 5)"></path> </clippath> </defs> <g transform="translate(-3 -5)"> <path d="M10.293,13.707a1,1,0,0,1,0-1.414L14.586,8H1A1,1,0,0,1,1,6H14.586L10.293,1.707A1,1,0,0,1,11.707.293l6,6a1,1,0,0,1,.172.231h0l.01.019,0,.005.007.014.006.012,0,.008.008.018v0a1,1,0,0,1-.009.817l0,0L17.9,7.44l0,.009-.005.011-.007.013,0,.008-.008.015,0,.005-.01.016,0,0-.011.017,0,0-.012.018,0,0-.012.017,0,0L17.8,7.6l0,0-.011.014,0,.006-.01.012-.009.011-.006.007-.015.017h0l-.04.042-6,6a1,1,0,0,1-1.414,0Z" transform="translate(3 5)" fill="currentColor"></path> </g> </svg></span></a> <div class="articleToolbarStatistics_articleToolbarStatistics__8_woN"> <div class="articleToolbarStatistics_column__R2GqD"> <div> <div> <span>的观点</年代pan> <div class="articleToolbarStatistics_amount__vJIDp"> 1618年</gydF4y2Badiv> </div> <div> <span>下载</年代pan> <div class="articleToolbarStatistics_amount__vJIDp"> 933年</gydF4y2Badiv> </div> </div> </div> <div class="articleToolbarStatistics_column__R2GqD articleToolbarStatistics_dimensions__pe7pO"> <div> 引用</gydF4y2Badiv> <span class="__dimensions_badge_embed__ articleToolbarStatistics_circle__p2dSc" data-doi="10.1155/2011/691058" data-style="small_circle"></span> </div> </div> <ul class="articleToolbarSocials_articleToolbarSocials__g02HH"> <li><a href="https://twitter.com/share?url=https://doi.org/10.1155/2011/691058&via=Hindawi" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="126.444 2.281 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