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no-repeat 6px;background-position:center;margin-top:10px;min-width:55px;display:none;} @media (min-width:768px){.hMPMVR .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .hMPMVR .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{-webkit-flex:9;-ms-flex:9;flex:9;text-align:left;padding:21px 37px 10px 0px;font-size:16px;font-weight:700;} @media (min-width:768px){.hMPMVR .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 10px 18px;}} @media (min-width:992px){.hMPMVR .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 10px 21px;}} .hMPMVR .floats-partial-section .floats-partial-footer .floats-partial-caption 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href="//www.newsama.com/journals/cmmm/" aria-label="Computational and Mathematical Methods in Medicine">计算和数学方法在医学</一个>/<一个class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/cmmm/contents/year/2019/" aria-label="2019">2019年</一个>/<span class="sc-bhlBdH UVThf">文章</span> </div> <div class="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 dDyxFF threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-eKZiaR dzZrgS section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</button> <div class="sc-bEjcJn jLUVhb static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-cbkKFq prcY sc-bGbJRg dVCLgr left_section_menu"> <p>在这一页上</p> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link 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sc-ePZHVD ewHMLz" href="#copyright" aria-label="">版权</一个></span> </div> </div> </div> <div class="threeColumn__ContentWrapper-sc-1bf4078-3 bbzREB contentWrapper"> <div class="threeColumn__Content-sc-1bf4078-4 jknsZc content"> <div class="articleContent__ArticleContentsWrapper-sc-2yl9jy-0 eSvjPB article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-2yl9jy-1 jntdRu article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-2yl9jy-2 hAzjHP"> <div class="sc-chbbiW mBGSe article_header_class"> <p class="sc-kZmsYB bkiEfx article_type">研究文章|开放获取</p> <div class="sc-RcBXQ ztvYg article_citation"> 体积 2019年 <span class="sc-fZwumE cUsFHx">|</span>文章的ID 4025305 <span class="sc-fZwumE cUsFHx">|</span> <a class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2019/4025305" aria-label="Doi-link">https://doi.org/10.1155/2019/4025305</一个> </div> <div class="sc-LKuAh lcOiDF article_full_citation"> <div class="sc-hzNEM gsmOCv isHide"> <p>克莱门特Roume萨玛Ezzina,休伯特痘痘,迪迪埃Delignieres, ”<span class="adjust-article-svg-size">偏见在分形过程的模拟和分析</span>”,<i>计算和数学方法在医学</我>, 卷。2019年, 文章的ID4025305, 12   页面, 2019年。 https://doi.org/10.1155/2019/4025305</p> </div> <button class="sc-hSdWYo etauus sc-iBEsjs kPshFw" color="">显示引用</button> </div> <h1 class="sc-iRbamj jZOxOO sc-iSDuPN hHHqqR article_title adjust-article-svg-size heading-title">偏见在分形过程的模拟和分析</h1> </div> <div class="sc-jrIrqw eHMFfo article_authors"> <hr class="sc-cEvuZC XkrFe hr__author"> <span class="">克莱门特Roume,<sup>1</sup></span> <span class="">萨玛Ezzina,<sup>1,2</sup></span> <span class="">休伯特痘痘,<sup>1,3</sup> 和</span> <span class=""><b>迪迪埃Delignieres</b><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-hjRWVT irNWJI icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a><a class="sc-htpNat bUhGXt link" href="https://orcid.org/0000-0002-7204-2272" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje iiusBg sc-iybRtq iQSObO" title="" role="presentation" src="data:image/svg+xml;base64,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" height="16"></a><sup>1</sup></span> <div class="sc-fHxwqH dMuGGA isHide"> <p><sup>1</sup><span>蒙彼利埃大学Euromov 700大道du图片圣人不定形铁块,34090年法国蒙彼利埃</span></p> <p><sup>2</sup><span>联盟国家运动的拉格朗日,狮子座150 des Poissonniers街,75883年法国巴黎</span></p> <p><sup>3</sup><span>内科老年病学,蒙彼利埃大学医院,39个查尔斯Flahault大道,34090年法国蒙彼利埃</span></p> </div> <button class="sc-hSdWYo etauus sc-iQtOjA kfDwZY" color="">显示更多</button> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</b>Marko Gosak</d我v> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</span> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2019年3月11日</span> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</span> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2019年6月20日</span> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</span> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2019年12月03</span> </div> </div> </div> <article class="sc-jtRlXQ hMPMVR article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4> <p>分形过程最近收到了越来越感兴趣,尤其是在康复领域。更确切地说,与衰老和疾病呈不规则碎片形的演变,表明复杂性,激发了大量的研究,试过了,例如,使患者分形的节奏。这类研究需要生成分形信号的相关方法和评估的呈不规则碎片形系列由参与者。在目前的工作,我们进行交叉验证的生成和三种方法分析的三种方法。我们生成精确的分形级数Davies-Harte (DH)算法,光谱合成方法(SSM), ARFIMA仿真方法。分析了系列通过去趋势波动分析(DFA),功率谱密度(PSD)方法,和ARFIMA模型。结果表明,一些方法一代现在的系统偏差:DH fBm系列提供了一个很强势的白噪声接近1 /<我>f</我>边界和导弹系列与预期指数更大的变化,与其他方法相比。相比之下,ARFIMA模拟提供相当准确的系列,没有偏见。论的方法分析,DFA系统倾向于低估fBm系列。相比之下,PSD产生高估了fBm系列。DFA,估计倾向于增加fGn系列的可变性,因为他们走到1 /<我>f</我>边界和fBm系列达到不可接受的水平。变异性是由PSD的最高水平。最后,ARFIMA方法生成的最好的系列和提供最准确,减少变量的估计。</p> <span class="end-abs"></span> <h4 id="introduction">1。介绍</h4> <p>生理或行为的重复测量事件(步耗时、心跳间隔和intertap间隔)通常表现为显著的变化。很长一段时间,这种可变性刚刚被认为是一种随机扰动,没有任何功能意义。然而,许多作者,在过去的二十年里,表明这些生物系列提供了一个典型的远程相关结构随着时间的推移,特别是统计自相似(分形)模式(<一个href="#B1">1</一个>- - - - - -<一个href="#B4">4</一个>]。分形过程最近收到了越来越感兴趣,尤其是在康复领域。更准确地说,呈不规则碎片形与衰老和疾病的演变,表明复杂性的损失(<一个href="#B5">5</一个>),激发了大量的研究,试过了,例如,使患者分形规律(<一个href="#B6">6</一个>- - - - - -<一个href="#B8">8</一个>]。</p> <p>作者在这一领域,面临着两个主要的方法论问题:第一个问题的评价的长程相关性水平生理系列。提出了许多不同的方法,和各自特点进行了有系统的比较研究[<一个href="#B9">9</一个>- - - - - -<一个href="#B12">12</一个>]。第二个是指准确的分形信号的生成必要的实验设备(节拍器和虚拟环境)控制远程相关性属性。等模拟的方法提出了系列(<一个href="#B13">13</一个>- - - - - -<一个href="#B15">15</一个>]。评估方法的评估,一方面,和模拟方法,另一方面,提出了一个典型的循环问题,表演,和偏见在前被分析的基础上,后者,反之亦然(<一个href="#B11">11</一个>]。发现偏差时,它仍然难以属性问题的方法模拟或评估的方法。为了克服这个问题,我们在本文中提出一个交叉验证研究,结合三种方法生成和三种方法的分析。</p> <p>我们首先提出一个正式的介绍的定义远程相关过程的三个主要领域:分数布朗运动框架(<一个href="#B16">16</一个>),光谱域(<一个href="#B17">17</一个>),自回归略微集成移动平均(ARFIMA)过程<一个href="#B18">18</一个>]。</p> <h4 id="theoretical-models">2。理论模型</h4> <h5 id="sec2.1">2.1。fBm / fGn模型</h5> <p>的<我>分数布朗运动</我>(fBm)表示<我>B</我><sub><i>H</我></sub>(<我>t</我>)是一个连续随机过程的数学模型引入了曼德布洛特和范·尼斯<一个href="#B16">16</一个>)作为一个泛化的布朗运动,增加不需要独立。<我>B</我><sub><i>H</我></sub>(<我>t</我>)的特点是赫斯特参数(<我>H</我>),它可以采取任何实际价值区间内)0,1 [。这个值给信息的性质和强度连续增量之间的关系。如果<我>H</我>低于0.5,<我>B</我><sub><i>H</我></sub>(<我>t</我>)是underdiffusive,其增量anticorrelated。相反,如果<我>H</我>高于0.5,<我>B</我><sub><i>H</我></sub>(<我>t</我>)是overdiffusive,它的增加呈正相关。如果<我>H</我>= 0.5,<我>B</我><sub>0.5</sub>(<我>t</我>)是一个普通的布朗运动(正常扩散),及其增量是一个不相关的高斯白噪声。</p> <p>fBm有一些基本属性。第一个是它的方差随着时间间隔的长度的幂函数,指数2<我>H</我>:<span class="equation_break" id="EEq1"><span class="left_break" id="L1"></span><span class="middle_break"><span class="center_break" id="M1"> <svg height="17.5784pt" id="M1-1" version="1.1" viewbox="0 0 65.834 17.5784" width="65.834pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B1-1"> <g transform="matrix(.013,0,0,-0.013,0,12.296)"> <path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 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103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path> </g> </g> </svg></span></span><span class="right_break" id="R1"> <svg class="label" height="11.44pt" id="M1-2" version="1.1" viewbox="0 0 13.398 11.44" width="13.398pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B1-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 611 70 451 70 272V271C70 90 136 -71 282 -169L300 -147Z" id="g190-41"></path> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M311 0V25C221 32 216 41 216 113V635C162 613 103 594 39 583V559L88 556C131 552 135 546 135 500V113C135 41 131 32 40 25V0H311Z" id="g190-213"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.9,9.26)"> <path d="M275 271C275 451 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 269V271Z" id="g190-42"></path> </g> </g> </svg></span></span>第二个是fBm分形过程,具有统计自相似性:<span class="equation_break" id="EEq2"><span class="left_break" id="L2"></span><span class="middle_break"><span class="center_break" id="M2"> <svg height="16.2605pt" id="M2-1" version="1.1" viewbox="0 0 104.744 16.2605" width="104.744pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B2-1"> <g transform="matrix(.013,0,0,-0.013,0,12.296)"> <path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,7.75,15.428)"> <use xlink:href="#g50-73"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.17,12.479)"> <path d="M300 -147C201 -63 143 98 143 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</g> </g> </svg> <svg class="alt_label" height="80.6794pt" id="IL6" version="1.1" viewbox="0 0 14.96 80.6794" width="14.96pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 34.41)" xlink:href="#B6-4"></use> </svg></span></span></p> <h5 id="sec2.2">2.2。谱模型</h5> <p>随机分形过程也可以被定义在频域,在此基础上的标度律有关(即力量。频率振幅平方),根据逆幂函数,指数<我>β</我>(<一个href="#B9">9</一个>,<一个href="#B10">10</一个>]。与指数一个fGn的过程<我>H</我>,功率谱可以表示如下<一个href="#B12">12</一个>,<一个href="#B19">19</一个>]:<span class="equation_break" id="EEq6"><span class="left_break" id="L7"></span><span class="middle_break"><span class="center_break" id="M7"> <svg height="29.5115pt" id="M7-1" version="1.1" viewbox="0 0 81.194 29.5115" width="81.194pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B7-1"> <g transform="matrix(.013,0,0,-0.013,0,16.857)"> <path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z" id="g113-84"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.31,16.857)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.33,16.857)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> </g> <g transform="matrix(.013,0,0,-0.013,21.69,16.857)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.37,16.857)"> <use xlink:href="#g113-29"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.36,8.349)"> <use xlink:href="#g113-50"></use> </g> <rect height="0.65243" width="31.0895" x="45.95" y="13.203"></rect> <g transform="matrix(.013,0,0,-0.013,45.95,26.082)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,54.3,21.906)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.73,21.906)"> <use xlink:href="#g50-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,66.44,21.906)"> <path d="M556 236V289H56V236H556Z" id="g54-33"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,72,21.906)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,78.23,16.857)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R7"> <svg class="label" height="11.44pt" id="M7-2" version="1.1" viewbox="0 0 15.428 11.44" width="15.428pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B7-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.26)"> <path d="M143 344C173 483 265 547 326 576C363 593 402 605 434 611L429 641C389 634 343 623 301 608C195 570 43 456 43 236C43 81 135 -12 245 -12C368 -12 453 88 453 208C453 310 380 393 273 393C253 393 232 386 211 376L143 344ZM234 338C325 338 367 255 367 172C367 102 346 21 264 21C184 21 132 113 132 239C132 267 133 291 138 312C164 327 197 338 234 338Z" id="g190-227"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.93,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>和相应的fBm过程<一个href="#B12">12</一个>,<一个href="#B20">20.</一个>]:<span class="equation_break" id="EEq7"><span class="left_break" id="L8"></span><span class="middle_break"><span class="center_break" id="M8"> <svg height="29.5115pt" id="M8-1" version="1.1" viewbox="0 0 81.194 29.5115" width="81.194pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B8-1"> <g transform="matrix(.013,0,0,-0.013,0,16.857)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.31,16.857)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.33,16.857)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.69,16.857)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.37,16.857)"> <use xlink:href="#g113-29"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.36,8.349)"> <use xlink:href="#g113-50"></use> </g> <rect height="0.65243" width="31.0895" x="45.95" y="13.203"></rect> <g transform="matrix(.013,0,0,-0.013,45.95,26.082)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,54.3,21.906)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.73,21.906)"> <use xlink:href="#g50-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,66.44,21.906)"> <path d="M556 236V289H337V504H275V289H56V236H275V-4H337V236H556Z" id="g54-36"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,72,21.906)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,78.23,16.857)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R8"> <svg class="label" height="11.44pt" id="M8-2" version="1.1" viewbox="0 0 15.028 11.44" width="15.028pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B8-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M430 623H48C43 580 39 534 30 478H57C80 544 84 550 152 550H369C286 366 187 178 74 -1L81 -12L156 -2C249 201 343 408 438 611L430 623Z" id="g190-223"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.53,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>然后fGn / fBm过程的功率谱的一般形式:<span class="equation_break" id="EEq8"><span class="left_break" id="L9"></span><span class="middle_break"><span class="center_break" id="M9"> <svg height="29.8847pt" id="M9-1" version="1.1" viewbox="0 0 64.344 29.8847" width="64.344pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B9-1"> <g transform="matrix(.013,0,0,-0.013,0,16.857)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.32,16.857)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.34,16.857)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.69,16.857)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.37,16.857)"> <use xlink:href="#g113-29"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.94,8.349)"> <use xlink:href="#g113-50"></use> </g> <rect height="0.65243" width="14.2371" x="45.95" y="13.203"></rect> <g transform="matrix(.013,0,0,-0.013,45.95,26.455)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,54.3,22.28)"> <path d="M563 583C563 664 501 710 433 710C381 710 334 692 285 648C212 582 178 506 149 350L74 -56C49 -190 36 -222 24 -226L30 -257C52 -256 95 -247 121 -229C131 -222 134 -206 165 -21L219 303C254 510 296 665 397 665C447 665 481 626 481 572C481 512 446 457 390 420C367 405 351 400 323 397L302 349C398 338 466 285 466 197C466 117 419 45 306 45C268 45 224 59 198 74L186 50C197 20 228 -14 274 -14C318 -14 359 3 401 26C478 68 554 144 554 225C554 322 493 367 412 396C490 446 563 500 563 583Z" id="g50-224"></path> </g> <g transform="matrix(.013,0,0,-0.013,61.38,16.857)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R9"> <svg class="label" height="11.44pt" id="M9-2" version="1.1" viewbox="0 0 15.168 11.44" width="15.168pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B9-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M246 635C138 635 67 554 67 471C67 401 116 348 178 315C143 296 103 268 87 252C65 231 42 203 42 157C42 50 128 -12 234 -12C319 -12 432 52 432 169C432 256 370 303 299 344C347 376 373 399 381 408C399 430 408 459 408 487C408 569 341 635 246 635ZM235 603C284 603 334 567 334 483C334 420 306 383 273 358C202 393 142 427 142 503C142 552 173 603 235 603ZM245 21C179 21 122 70 122 163C122 219 155 270 204 300C279 263 352 219 352 144C352 66 308 21 245 21Z" id="g190-152"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.67,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>与<我>β</我>∈]−1,1 (fGn和<我>β</我>∈]1,3 (fBm。这表明fGn fBm可以视为连续介质,双方家庭是在时域特征标度指数<我>α</我>,<我>α</我>=<我>H</我>fGn和<我>α</我>=<我>H</我>fBm + 1。这个假设已经被彭et al。<一个href="#B4">4</一个>在去趋势波动分析的概念(见部分<一个href="#sec3">3</一个>)。的标度指数<我>α</我>线性相关光谱指数吗<我>β</我>在整个fGn / fBm连续<span class="inline_break"> <svg height="12.7178pt" id="M10" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 47.044 12.7178" width="47.044pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z" id="g113-223"></path> </g> <g transform="matrix(.013,0,0,-0.013,11.017,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.28,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.778,0)"> <path d="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z" id="g113-224"></path> </g> <g transform="matrix(.013,0,0,-0.013,39.413,0)"> <use xlink:href="#g117-36"></use> </g> </svg><span class="ibiop"></span> <svg height="12.7178pt" style="vertical-align:-3.42947pt" version="1.1" viewbox="52.0751838 -9.28833 11.596 12.7178" width="11.596pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,52.125,0)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.365,0)"> <path d="M368 703H309L44 -163H104L368 703Z" id="g113-48"></path> </g> </svg><span class="isep"></span> <svg height="12.7178pt" style="vertical-align:-3.42947pt" version="1.1" viewbox="63.6761838 -9.28833 11.044 12.7178" width="11.044pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,63.726,0)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,69.966,0)"> <use xlink:href="#g113-42"></use> </g> </svg></span>(<一个href="#B21">21</一个>]。这个案子<我>β</我>= 1定义了所谓的“1 /<我>f</我>噪音,”代表fGn和fBm过程之间的边界。</p> <h5 id="sec2.3">2.3。ARFIMA模型</h5> <p>第三种方法远程相关流程提供的自回归略微集成移动平均(ARFIMA)模型(<一个href="#B18">18</一个>]。这种方法是一个扩展的ARIMA(集成,自回归移动平均)框架,引入了盒等。<一个href="#B22">22</一个>),旨在代表不同的时间序列的短期关系。ARIMA模型可能由三部分组成的。自回归组件表明当前的观测<我>y</我>(<我>t</我>)的加权和<svg height="10.2124pt" id="M11" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 7.83752 10.2124" 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transform="matrix(.013,0,0,-0.013,153.18,22.3)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,159.89,22.118)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="37.8457pt" id="I12" version="1.1" viewbox="0 0 162.86 37.8457" width="162.86pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B12-1"></use> </svg></span></span><span class="right_break" id="R12"> <svg class="label" height="11.44pt" id="M12-2" version="1.1" viewbox="0 0 15.338 11.44" width="15.338pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B12-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M247 635C117 635 41 518 41 422C41 317 114 239 220 239C239 239 256 244 278 255L348 290C315 139 207 37 63 13L67 -15C93 -15 155 -5 207 17C343 71 443 203 443 385C443 520 371 635 247 635ZM231 602C331 602 355 476 355 390C355 371 354 349 351 325C334 310 298 294 261 294C177 294 128 369 128 457C128 516 155 602 231 602Z" id="g190-193"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.84,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="37.8457pt" id="IL12" version="1.1" viewbox="0 0 15.39 37.8457" width="15.39pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 12.99)" xlink:href="#B12-2"></use> </svg></span></span></p> <p>移动平均线组件认为,当前观测取决于随机扰动影响的价值<我>问</我>前观察,再加上自己的具体的微扰:<span class="equation_break" id="EEq10"><span class="left_break" id="L13"></span><span class="middle_break"><span class="center_break" id="M13"> <svg height="37.2611pt" id="M13-1" version="1.1" viewbox="0 0 159.784 37.2611" width="159.784pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B13-1"> <g transform="matrix(.013,0,0,-0.013,0,21.533)"> <use xlink:href="#g113-122"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.71,21.716)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.22,21.533)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.66,21.716)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.82,21.533)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,43.14,5.65)"> <path d="M481 430L460 436C440 442 393 451 366 451C348 451 325 448 313 446C267 437 195 409 147 367C79 308 24 211 24 105C24 37 56 -12 93 -12C121 -12 156 1 199 32C246 66 313 122 349 168H351L286 -147C274 -205 261 -215 210 -224L199 -226L193 -255L438 -243L442 -214L417 -212C364 -208 359 -200 370 -140L433 204C455 324 469 389 481 430ZM391 385C382 336 366 260 358 238C321 178 209 59 143 59C129 59 115 83 115 131C115 207 152 317 220 373C243 392 282 403 314 403C348 403 374 395 391 385Z" id="g50-114"></path> </g> <g transform="matrix(.013,0,0,-0.013,38.84,21.54)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.08,35.666)"> <use xlink:href="#g50-108"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.72,35.666)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,48.28,35.666)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.76,21.533)"> <path d="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z" id="g113-230"></path> </g> <g transform="matrix(.013,0,0,-0.013,61.42,21.716)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.93,21.533)"> <use xlink:href="#g113-108"></use> </g> <g transform="matrix(.013,0,0,-0.013,72.47,21.716)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,79.19,21.533)"> <use xlink:href="#g113-247"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.7,21.716)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,91.21,21.533)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,98.55,21.533)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,109.09,21.533)"> <use xlink:href="#g113-108"></use> </g> <g transform="matrix(.013,0,0,-0.013,115.63,21.716)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,123.12,21.533)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,133.65,21.533)"> <use xlink:href="#g113-247"></use> </g> <g transform="matrix(.013,0,0,-0.013,141.17,21.716)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,145.68,21.533)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,150.11,21.716)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,156.82,21.533)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="37.2611pt" id="I13" version="1.1" viewbox="0 0 159.79 37.2611" width="159.79pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B13-1"></use> </svg></span></span><span class="right_break" id="R13"> <svg class="label" height="11.44pt" id="M13-2" version="1.1" viewbox="0 0 19.728 11.44" width="19.728pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B13-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.82,9.26)"> <path d="M248 635C97 635 43 457 43 311C43 153 97 -12 247 -12S450 166 450 312C450 466 397 635 248 635ZM246 603C337 603 361 452 361 312S337 20 248 20S132 172 132 313C132 452 156 603 246 603Z" id="g190-254"></path> </g> <g transform="matrix(.013,0,0,-0.013,15.23,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="37.2611pt" id="IL13" version="1.1" viewbox="0 0 19.81 37.2611" width="19.81pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 12.7)" xlink:href="#B13-2"></use> </svg></span></span></p> <p>最后,差分参数<我>d</我>表明差分的数量应该应用于建模前的系列。ARIMA模型的结合这三个组件,可以各自指定的订单的三个过程(<我>p</我>,<我>d</我>,<我>问</我>)。ARIMA模型被用于生成时间序列指定<我>p</我>,<我>d</我>,<我>问</我>参数或确定最好的<我>p</我>,<我>d</我>,<我>问</我>结合会计对于一个给定的系列(<一个href="#B22">22</一个>,<一个href="#B23">23</一个>]。</p> <p>ARIMA模型可以更方便地使用所谓的表达<我>二次变换算符</我>,定义为<span class="equation_break" id="EEq11"><span class="left_break" id="L14"></span><span class="middle_break"><span class="center_break" id="M14"> <svg height="13.8661pt" id="M14-1" 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xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.95,9.367)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.11,9.184)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.38,9.184)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.013,0,0,-0.013,54.82,9.367)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.34,9.184)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.68,9.184)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.21,9.184)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,83.45,9.367)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.21,9.184)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R14"> <svg class="label" height="11.44pt" id="M14-2" version="1.1" viewbox="0 0 17.788 11.44" width="17.788pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B14-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.9,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.29,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>通用ARIMA (<我>p</我>,<我>d</我>,<我>问</我>)模型可以写成<span class="equation_break" id="EEq12"><span class="left_break" id="L15"></span><span class="middle_break"><span class="center_break" id="M15"> <svg height="16.7446pt" id="M15-1" version="1.1" viewbox="0 0 164.674 16.7446" width="164.674pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B15-1"> <g transform="matrix(.013,0,0,-0.013,0,12.78)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.52,12.963)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.04,12.78)"> <use xlink:href="#g113-67"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.85,12.963)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.58,12.963)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.09,12.78)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.24,12.78)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.77,12.78)"> <use xlink:href="#g113-67"></use> </g> <g transform="matrix(.013,0,0,-0.013,60.59,12.963)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,65.18,6.517)"> <path d="M538 684C542 703 539 710 529 710C512 710 455 682 363 674L361 644H396C444 644 448 642 438 594L405 438C373 450 347 451 336 451C288 451 200 416 147 374C69 312 24 207 24 113C24 29 60 -12 94 -12C126 -12 156 4 196 30C231 53 296 100 346 166H348L328 81C311 10 325 -12 348 -12C380 -12 450 24 512 98L495 125C466 97 431 70 417 70C408 70 408 80 411 98L538 684ZM390 373L361 240C336 196 210 56 145 56C132 56 113 73 113 131C113 216 156 338 220 379C243 394 266 402 303 402C331 402 375 388 390 373Z" id="g50-101"></path> </g> <g transform="matrix(.013,0,0,-0.013,73.01,12.78)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.46,12.963)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.97,12.78)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,91.41,12.963)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,99.57,12.78)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,110.83,12.78)"> <use xlink:href="#g113-230"></use> </g> <g transform="matrix(.013,0,0,-0.013,119.49,12.963)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,124,12.78)"> <use xlink:href="#g113-67"></use> </g> <g transform="matrix(.013,0,0,-0.013,131.81,12.963)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,138.54,12.78)"> <use xlink:href="#g113-247"></use> </g> <g transform="matrix(.013,0,0,-0.013,146.05,12.963)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,150.56,12.78)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,155,12.963)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,161.71,12.78)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="16.7446pt" id="I15" version="1.1" viewbox="0 0 164.67 16.7446" width="164.67pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B15-1"></use> </svg></span></span><span class="right_break" id="R15"> <svg class="label" height="11.44pt" id="M15-2" version="1.1" viewbox="0 0 19.468 11.44" width="19.468pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B15-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.93,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.97,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="16.7446pt" id="IL15" version="1.1" viewbox="0 0 19.54 16.7446" width="19.54pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 2.44)" xlink:href="#B15-2"></use> </svg></span></span>在哪里<我>ϕ</我>(<我>B</我>),<我>θ</我>(<我>B</我>分别是自回归和移动平均线运营商,在二次变换算符表示为多项式:<svg height="15.0208pt" id="M16" style="vertical-align:-3.429399pt" version="1.1" viewbox="-0.0498162 -11.5914 218.768 15.0208" width="218.768pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.346,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.844,0)"> <use xlink:href="#g113-67"></use> </g> <g transform="matrix(.013,0,0,-0.013,19.658,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.787,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,39.05,0)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,48.196,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.732,0)"> <use xlink:href="#g113-67"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.545,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,73.892,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,78.39,0)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,84.63,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,92.033,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,102.57,0)"> <use xlink:href="#g113-67"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,110.383,-5.741)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,115.329,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,122.675,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,127.173,0)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,133.413,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,140.817,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,151.353,0)"> <path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 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transform="matrix(.013,0,0,-0.013,76.648,0)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.888,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.291,0)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,103.003,0)"> <use xlink:href="#g113-67"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,110.816,-5.741)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,115.763,0)"> <use xlink:href="#g113-230"></use> </g> <g transform="matrix(.013,0,0,-0.013,122.238,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,126.736,0)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,132.976,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,140.379,0)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,150.916,0)"> <use xlink:href="#g113-46"></use> </g> <g transform="matrix(.013,0,0,-0.013,156.059,0)"> <use xlink:href="#g113-46"></use> </g> <g transform="matrix(.013,0,0,-0.013,161.202,0)"> <use xlink:href="#g113-46"></use> </g> <g transform="matrix(.013,0,0,-0.013,167.105,0)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,177.641,0)"> <use xlink:href="#g113-67"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,185.454,-5.741)"> <use xlink:href="#g50-114"></use> </g> <g transform="matrix(.013,0,0,-0.013,190.511,0)"> <use xlink:href="#g113-230"></use> </g> <g transform="matrix(.013,0,0,-0.013,196.986,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,201.484,0)"> <path d="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z" id="g113-114"></path> </g> <g transform="matrix(.013,0,0,-0.013,207.867,0)"> <use xlink:href="#g113-42"></use> </g> </svg>(<一个href="#B24">24</一个>]。在模型的初始配方,<我>d</我>参数是一个整数<一个href="#B22">22</一个>]。格兰杰和Joyeux<一个href="#B18">18</一个>)表明,它有可能为这个模型提供远程依赖属性允许差分参数<我>d</我>承担部分值,从而获得一个ARFIMA模型。</p> <p>在这里,我们专注于最简单的ARFIMA模型(0,<我>d</我>,0),这应该只包含远程相关性。这个模型使用二次变换操作符符号,表示如下(<一个href="#B25">25</一个>]:<span class="equation_break" id="EEq13"><span class="left_break" id="L18"></span><span class="middle_break"><span class="center_break" id="M18"> <svg height="16.7446pt" id="M18-1" version="1.1" viewbox="0 0 108.384 16.7446" width="108.384pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B18-1"> <g transform="matrix(.013,0,0,-0.013,0,12.963)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.51,12.78)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.66,12.78)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.19,12.78)"> <use xlink:href="#g113-67"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.01,12.963)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,36.6,6.517)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,44.43,12.78)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.88,12.963)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.39,12.78)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,62.82,12.963)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,70.99,12.78)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.25,12.78)"> <use xlink:href="#g113-247"></use> </g> <g transform="matrix(.013,0,0,-0.013,89.76,12.963)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,94.28,12.78)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,98.71,12.963)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,105.42,12.78)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R18"> <svg class="label" height="11.44pt" id="M18-2" version="1.1" viewbox="0 0 19.258 11.44" width="19.258pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B18-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.89,9.26)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.76,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>与<span class="equation_break" id="EEq14"><span class="left_break" id="L19"></span><span class="middle_break"><span class="center_break" id="M19"> <svg height="36.1428pt" id="M19-1" version="1.1" viewbox="0 0 151.734 36.1428" width="151.734pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B19-1"> <g transform="matrix(.013,0,0,-0.013,0,20.598)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.51,20.415)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.66,20.415)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.2,20.415)"> <use xlink:href="#g113-67"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.01,20.598)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,36.6,14.152)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.89,20.415)"> <use xlink:href="#g117-34"></use> </g> <g 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viewbox="0 0 151.74 36.1428" width="151.74pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B19-1"></use> </svg></span></span><span class="right_break" id="R19"> <svg class="label" height="11.44pt" id="M19-2" version="1.1" viewbox="0 0 19.638 11.44" width="19.638pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B19-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.68,9.26)"> <use xlink:href="#g190-166"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.14,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="36.1428pt" id="IL19" version="1.1" viewbox="0 0 19.71 36.1428" width="19.71pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 12.14)" xlink:href="#B19-2"></use> </svg></span></span></p> <p>格兰杰和Joyeux<一个href="#B18">18</一个>)获得一个过滤器<我>一个</我>(<我>B</我>从方程()<一个href="#EEq13">13</一个>)和(<一个href="#EEq14">14</一个>)和证明过程可以写成<span class="equation_break" id="EEq15"><span class="left_break" id="L20"></span><span class="middle_break"><span class="center_break" id="M20"> <svg height="74.482pt" id="M20-1" version="1.1" viewbox="0 0 89.148 74.482" width="89.148pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B20-1"> <g transform="matrix(.013,0,0,-0.013,0,20.415)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.45,20.598)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.96,20.415)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.4,20.598)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.56,20.415)"> <use 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<p>我们使用生成的三种方法:Davies-Harte算法,光谱合成方法,ARFIMA模拟方法。这些方法在下面会详细进行介绍。为每一个选择<我>α</我>值和每个方法,我们生成的120系列的1024数据点。在本节中,所有方法都写在离散时间和频域;为阅读方便,我们把变量<我>t</我>离散时间域和<我>f</我>对于离散的频域。</p> <h5 id="sec3.1">3.1。Davies-Harte算法(DH)</h5> <p>我们使用了戴维斯和哈特提出的算法<一个href="#B13">13</一个>),生成一系列fGn的长度<我>N</我>(<我>N</我>2)的力量。正如前面指出的,一个fGn的过程是完全被其自协方差函数(见方程(<一个href="#EEq5">5</一个>))。然后,可以推断出准确的光谱功率<我>年代</我>预期的自协方差函数,离散傅里叶变换后的序列的协方差值<我>γ</我><sub><i>G</我>1</sub>由方程(<一个href="#EEq5">5</一个>):<我>γ</我><sub><i>G</我>1</sub>(0)<我>γ</我><sub><i>G</我>1</sub>(1)、…<我>γ</我><sub><i>G</我>1</sub>((<我>N</我>/ 2)−1);<我>γ</我><sub><i>G</我>1</sub>(<我>N</我>/ 2),<我>γ</我><sub><i>G</我>1</sub>((<我>N</我>/ 2)−1)、…<我>γ</我><sub><i>G</我>1</sub>(1):<span class="equation_break" id="EEq18"><span class="left_break" id="L22"></span><span class="middle_break"><span class="center_break" id="M22"> <svg height="40.1566pt" id="M22-1" version="1.1" viewbox="0 0 26.695 40.1566" width="26.695pt" xmlns="http://www.w3.org/2000/svg" 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xlink:href="#g50-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,148.74,23.04)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="109.741pt" id="I22" version="1.1" viewbox="0 0 169.61 109.741" width="169.61pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -12.45)" xlink:href="#B22-1"></use> <use transform="matrix(1 0 0 1 3.63 23.43)" xlink:href="#B22-2"></use> <use transform="matrix(1 0 0 1 17.83 69.59)" xlink:href="#B22-3"></use> </svg></span></span><span class="right_break" id="R22"> <svg class="label" height="11.44pt" id="M22-4" version="1.1" viewbox="0 0 19.498 11.44" width="19.498pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B22-4"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.83,9.26)"> <use xlink:href="#g190-152"></use> </g> <g transform="matrix(.013,0,0,-0.013,15,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="109.741pt" id="IL22" version="1.1" viewbox="0 0 19.58 109.741" width="19.58pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 48.94)" xlink:href="#B22-4"></use> </svg></span></span>在哪里<我>f</我>= 0,1,…,<我>N</我>−1。检查是很重要的<svg height="12.7178pt" id="M23" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 44.8524 12.7178" width="44.8524pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.013,0,0,-0.013,6.136,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.634,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.986,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.116,0)"> <path d="M531 285V335L57 550V494L473 310L57 127V71L531 285ZM531 -40V10H57V-40H531Z" id="g117-94"></path> </g> <g transform="matrix(.013,0,0,-0.013,38.379,0)"> <use xlink:href="#g113-49"></use> </g> </svg>对所有<我>f</我>。消极会表明,序列是无效的。</p> <p>让<span class="nowrap"> <svg height="14.8173pt" id="M24" style="vertical-align:-5.52897pt" version="1.1" viewbox="-0.0498162 -9.28833 38.139 14.8173" width="38.139pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M962 650H739L732 622L760 619C812 613 819 604 798 552C760 457 671 267 606 131H604L511 638H480L237 131H233L183 554C177 607 183 614 226 619L248 622L257 650H24L17 622C88 615 92 611 103 524L173 -11H203L450 491H453L543 -11H575L839 529C882 609 886 613 953 622L962 650Z" id="g113-88"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.132)"> <path d="M463 437C426 431 375 425 327 422C297 440 264 449 231 449H230C153 449 51 396 51 283C51 215 94 168 139 149C123 129 91 103 51 88C50 78 53 60 62 46C75 25 100 2 136 -9C112 -28 73 -59 53 -79C38 -94 29 -113 29 -135C30 -192 91 -257 203 -257C336 -257 452 -160 452 -59C452 39 371 59 309 59C275 59 240 58 203 58C158 58 140 77 140 96C140 110 157 129 170 138C186 135 205 133 221 133C306 133 396 185 396 293C396 328 384 360 366 381L423 378C439 387 459 413 468 429L463 437ZM219 418C277 418 314 362 314 284C314 205 275 166 231 165C176 165 137 221 137 299C137 376 177 418 219 418ZM241 -11C285 -11 314 -14 339 -24C367 -36 384 -61 384 -95C384 -157 335 -206 240 -206C166 -206 108 -165 108 -110C108 -82 128 -54 154 -32C172 -17 195 -11 241 -11Z" id="g190-104"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,15.082,3.132)"> <use xlink:href="#g190-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.592,0)"> <use xlink:href="#g113-41"></use> </g> <g 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transform="matrix(.013,0,0,-0.013,42.41,22.233)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.81,22.233)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.84,22.233)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,67.19,22.233)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.42,22.233)"> <use xlink:href="#g113-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,79.8,15.969)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,82.35,15.969)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,86.78,15.969)"> <use xlink:href="#g50-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,91.24,15.969)"> <use xlink:href="#g50-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,97.11,15.969)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,100.37,15.969)"> <path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z" id="g50-117"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,103.52,15.969)"> <use xlink:href="#g50-48"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,107.43,15.969)"> <use xlink:href="#g50-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,115.19,15.969)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,119.08,22.233)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="65.1429pt" id="I26" version="1.1" viewbox="0 0 148.72 65.1429" width="148.72pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -10.12)" xlink:href="#B26-1"></use> <use transform="matrix(1 0 0 1 26.59 24.94)" xlink:href="#B26-2"></use> </svg></span></span><span class="right_break" id="R26"> <svg class="label" height="11.44pt" id="M26-3" version="1.1" viewbox="0 0 21.518 11.44" width="21.518pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B26-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.61,9.26)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.02,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="65.1429pt" id="IL26" version="1.1" viewbox="0 0 21.6 65.1429" width="21.6pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 26.64)" xlink:href="#B26-3"></use> </svg></span></span>在哪里<我>t</我>= 1,2,…<我>N</我>。</p> <p>我们首先生成fGn系列<我>H</我>值从0.1到0.9,0.1的步骤。为了探索更准确的DFA的性能接近1 /<我>f</我>边界,我们也生成fGn系列<我>H</我>值从0.91到0.99,0.01的步骤。第二组fGn系列生成,<我>H</我>值从0.1到0.9,0.1的步骤,综合获取fBm每个相应的系列<我>H</我>值(即。,因为<我>α</我>值从1.1到1.9)。最后,我们生成的fGn系列<我>H</我>从0.01到0.09,综合他们获取fBm系列接近1 /<我>f</我>边界(即。,因为<我>α</我>值从1.01到1.09)。</p> <h5 id="sec3.2">3.2。谱合成方法(SSM)</h5> <p>谱合成方法设计生产fBm和fGn系列<我>x</我>(<我>t</我>基于功率谱密度的特点<我>年代</我>(<我>f</我>这些信号。换句话说,导弹的想法是生成一种权利<我>年代</我>(<我>f</我>),产生了fBm或fGn指数0<我><</我><i>H</我><i><</我>1。</p> <p>自<我>年代</我>(<我>f</我>)获得的平方模数信号的傅里叶变换及其成正比<svg height="15.6876pt" id="M27" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -12.2582 19.9177 15.6876" width="19.9177pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.352,-5.741)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.912,-5.741)"> <use xlink:href="#g50-224"></use> </g> </svg>(见方程(<一个href="#EEq8">8</一个>)),<span class="equation_break" id="EEq21"><span class="left_break" id="L28"></span><span class="middle_break"><span class="center_break" id="M28"> <svg height="17.1152pt" id="M28-1" version="1.1" viewbox="0 0 124.804 17.1152" width="124.804pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B28-1"> <g transform="matrix(.013,0,0,-0.013,0,13.151)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.31,13.151)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.34,13.151)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.69,13.151)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.37,13.151)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.63,6.483)"> <path d="M162 0V316H101V0H162Z" id="g119-34"></path> </g> <g transform="matrix(.013,0,0,-0.013,41.63,10.084)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.63,13.686)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.63,17.287)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.06,13.151)"> <path d="M748 650H522L515 622L546 617C580 611 587 604 565 575C518 513 469 451 419 393C376 474 349 534 330 580C318 609 325 612 361 618L383 622L392 650H151L144 622C214 616 224 612 257 543L360 327C270 218 187 124 159 95C106 40 92 34 26 28L17 0H252L259 28L236 31C189 37 188 47 209 78C249 136 308 210 377 294L478 79C494 44 487 37 449 32L418 28L409 0H673L680 28C596 34 591 39 554 116L436 361C526 469 574 521 604 553C659 612 669 614 739 622L748 650Z" id="g113-89"></path> </g> <g transform="matrix(.013,0,0,-0.013,57.19,13.151)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,62.21,13.151)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,70.56,13.151)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,75.61,6.483)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,75.61,10.084)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,75.61,13.686)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,75.61,17.287)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,79.08,5.85)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,87.66,13.151)"> <use xlink:href="#g113-29"></use> </g> <g transform="matrix(.013,0,0,-0.013,102.04,13.151)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,110.39,6.887)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,115.95,6.887)"> <use xlink:href="#g50-224"></use> </g> <g transform="matrix(.013,0,0,-0.013,121.84,13.151)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R28"> <svg class="label" height="11.44pt" id="M28-2" version="1.1" viewbox="0 0 19.468 11.44" width="19.468pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B28-2"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.25)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.58,9.25)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.97,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>我们需要生成一系列复杂<我>X</我>(<我>f</我>与模量)<我>r</我>(<我>f</我>1 /)成正比<我>f</我><sup><i>β</我>/ 2</sup>。<我>r</我>(<我>f</我>)方法如下:<span class="equation_break" id="EEq22"><span class="left_break" id="L29"></span><span class="middle_break"><span class="center_break" id="M29"> <svg height="34.7113pt" id="M29-1" version="1.1" viewbox="0 0 87.584 34.7113" width="87.584pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B29-1"> <g transform="matrix(.013,0,0,-0.013,0,21.683)"> <path d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z" id="g113-115"></path> </g> <g transform="matrix(.013,0,0,-0.013,7.67,21.683)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.7,21.683)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.05,21.683)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.73,21.683)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.19,10.593)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,52.96,13.725)"> <use xlink:href="#g190-104"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,57.27,13.725)"> <use xlink:href="#g190-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,64.96,10.593)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,69.98,10.593)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,78.33,10.593)"> <use xlink:href="#g119-6"></use> </g> <rect height="0.65243" width="41.2363" x="42.19" y="18.03"></rect> <g transform="matrix(.013,0,0,-0.013,51.5,31.282)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.85,27.106)"> <use xlink:href="#g50-224"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,65.2,27.106)"> <use xlink:href="#g50-48"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.1,27.106)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,84.62,21.683)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R29"> <svg class="label" height="11.44pt" id="M29-2" version="1.1" viewbox="0 0 21.158 11.44" width="21.158pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B29-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.61,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.66,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>在哪里<我>W</我><sub>gn</sub>是一个高斯白噪声和<我>f</我>频率范围从1到吗<我>N</我>/ 2。</p> <p>生成<我>X</我>(<我>f</我>),我们也需要生成一个随机相位弧度:<span class="equation_break" id="EEq23"><span class="left_break" id="L30"></span><span class="middle_break"><span class="center_break" id="M30"> <svg height="14.5707pt" id="M30-1" version="1.1" viewbox="0 0 80.854 14.5707" width="80.854pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B30-1"> <g transform="matrix(.013,0,0,-0.013,0,10.593)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.52,10.593)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.55,10.593)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.9,10.593)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.58,10.593)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.84,10.593)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.08,10.593)"> <path d="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 379 25 341L43 318C81 354 121 372 181 372C161 246 87 53 23 3L30 -12C48 -12 88 -4 113 11C157 75 207 248 232 371L386 367L326 109C321 86 318 66 318 50C318 4 339 -12 366 -12C410 -12 461 21 505 69L492 96C467 79 434 60 418 60C406 60 400 78 411 147C422 217 439 300 457 366C487 366 524 367 536 370C547 385 558 408 574 449Z" id="g113-238"></path> </g> <g transform="matrix(.013,0,0,-0.013,56.77,10.593)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,67.54,13.725)"> <path d="M518 50L491 51C452 54 444 60 444 110V444C429 441 405 437 377 434C348 430 314 427 287 426V403L323 397C356 392 365 386 365 333V99C331 66 293 51 257 51C212 51 169 75 169 164V299C169 366 169 413 172 444C156 441 128 437 101 433C75 430 50 427 29 426V403L57 397C82 391 90 386 90 333V137C90 29 147 -12 214 -12C241 -12 262 -4 291 13S342 48 365 65V-6L371 -12C390 -7 415 1 441 8C468 15 496 21 518 24V50Z" id="g190-118"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,72.37,13.725)"> <use xlink:href="#g190-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.89,10.593)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R30"> <svg class="label" height="11.44pt" id="M30-2" version="1.1" viewbox="0 0 21.018 11.44" width="21.018pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B30-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.64,9.26)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.52,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>在哪里<我>W</我><sub>联合国</sub>是一个均匀分布的白噪声。</p> <p>我们可以创建复杂系数:<span class="equation_break" id="EEq24"><span class="left_break" id="L31"></span><span class="middle_break"><span class="center_break" id="M31"> <svg height="37.9821pt" id="M31-1" version="1.1" viewbox="0 0 124.764 37.9821" width="124.764pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B31-1"> <g transform="matrix(.013,0,0,-0.013,0,10.593)"> <use xlink:href="#g113-98"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.76,10.593)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.78,10.593)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.13,10.593)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.81,10.593)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.08,10.593)"> <use xlink:href="#g113-115"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.74,10.593)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,54.77,10.593)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.12,10.593)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,70.35,10.593)"> <use xlink:href="#g121-97"></use> </g> <g transform="matrix(.013,0,0,-0.013,75.85,10.593)"> <use xlink:href="#g121-109"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.48,10.593)"> <path d="M319 325C317 349 306 409 297 431C277 440 250 449 209 449C117 449 57 389 57 319C57 243 122 209 182 182C232 159 261 135 261 91C261 48 227 21 190 21C130 21 85 79 68 145L41 140C41 104 51 36 58 22C75 7 121 -12 172 -12C252 -12 337 35 337 126C337 195 286 231 210 262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z" id="g121-113"></path> </g> <g transform="matrix(.013,0,0,-0.013,91.67,10.593)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,101.19,10.593)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,106.22,10.593)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,114.57,10.593)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,121.8,10.593)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="37.9821pt" id="M31-2" version="1.1" viewbox="0 0 122.744 37.9821" width="122.744pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B31-2"> <g transform="matrix(.013,0,0,-0.013,0,34.018)"> <path d="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z" id="g113-99"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.28,34.018)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.3,34.018)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.66,34.018)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.34,34.018)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.6,34.018)"> <use xlink:href="#g113-115"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.27,34.018)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,54.29,34.018)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,62.64,34.018)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,69.87,34.018)"> <use xlink:href="#g121-113"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.64,34.018)"> <path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z" id="g121-103"></path> </g> <g transform="matrix(.013,0,0,-0.013,78.13,34.018)"> <path d="M524 0V26C466 32 460 36 460 104V297C460 393 411 449 331 449C302 449 276 437 248 419C223 402 201 387 181 372V451C137 432 90 420 42 411V388C96 378 102 374 102 310V104C102 38 97 33 29 26V0H246V26C187 32 181 36 181 104V339C211 365 250 390 290 390C357 390 381 345 381 276V109C381 40 374 32 315 26V0H524Z" id="g121-108"></path> </g> <g transform="matrix(.013,0,0,-0.013,89.65,34.018)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,99.17,34.018)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,104.2,34.018)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,112.55,34.018)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,119.78,34.018)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R31"> <svg class="label" height="11.44pt" id="M31-3" version="1.1" viewbox="0 0 21.318 11.44" width="21.318pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B31-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.36,9.26)"> <use xlink:href="#g190-166"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.82,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>这些系数是扩展到整个范围的预期值(对香农定理),<我>一个</我>(<我>f</我>)<span class="inline_break"> <svg height="11.5564pt" id="M32" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 20.764 11.5564" width="20.764pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.498,0)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.408,0)"> <use xlink:href="#g113-48"></use> </g> </svg><span class="isep"></span> <svg height="11.5564pt" style="vertical-align:-2.26807pt" version="1.1" viewbox="20.7191838 -9.28833 32.857 11.5564" width="32.857pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,20.769,0)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.009,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.413,0)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.124,0)"> <use xlink:href="#g113-50"></use> </g> </svg></span>来<我>N</我>等于<我>一个</我>(<我>f</我>)(<我>N</我>/ 1和2)<我>b</我>(<我>f</我>)<span class="inline_break"> <svg height="11.5564pt" id="M33" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 20.764 11.5564" width="20.764pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.498,0)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.408,0)"> <use xlink:href="#g113-48"></use> </g> </svg><span class="isep"></span> <svg height="11.5564pt" style="vertical-align:-2.26807pt" version="1.1" viewbox="20.7191838 -9.28833 32.857 11.5564" width="32.857pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,20.769,0)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.009,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.413,0)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.124,0)"> <use xlink:href="#g113-50"></use> </g> </svg></span>来<我>N</我>等于<我>b</我>(<我>f</我>)(<我>N</我>/ 2)1。然后,复杂的系列<我>X</我>(<我>f</我>)生成如下:<span class="equation_break" id="EEq25"><span class="left_break" id="L34"></span><span class="middle_break"><span class="center_break" id="M34"> <svg height="14.5707pt" id="M34-1" version="1.1" viewbox="0 0 121.464 14.5707" width="121.464pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B34-1"> <g transform="matrix(.013,0,0,-0.013,0,10.593)"> <use xlink:href="#g113-89"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.12,10.593)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.15,10.593)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.5,10.593)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.18,10.593)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.44,10.593)"> <use xlink:href="#g113-98"></use> </g> <g transform="matrix(.013,0,0,-0.013,54.2,10.593)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.23,10.593)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,67.58,10.593)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,75.53,10.593)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.07,10.593)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,89.62,10.593)"> <use xlink:href="#g113-99"></use> </g> <g transform="matrix(.013,0,0,-0.013,97.9,10.593)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,102.92,10.593)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,111.27,10.593)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,118.5,10.593)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R34"> <svg class="label" height="11.44pt" id="M34-2" version="1.1" viewbox="0 0 21.078 11.44" width="21.078pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B34-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.68,9.26)"> <use xlink:href="#g190-161"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.58,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>最后,这个复数的傅里叶反变换计算获得时间序列:<span class="equation_break" id="EEq26"><span class="left_break" id="L35"></span><span class="middle_break"><span class="center_break" id="M35"> <svg height="40.1984pt" id="M35-1" version="1.1" viewbox="0 0 104.599 40.1984" width="104.599pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B35-1"> <g transform="matrix(.013,0,0,-0.013,0,22.233)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.45,22.415)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.96,22.233)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.4,22.415)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.56,22.233)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.82,22.233)"> <path d="M999 699C953 675 891 661 855 661C748 661 620 699 509 699C417 699 340 690 280 658C208 619 162 568 162 495C162 432 198 383 245 358C274 343 303 336 334 336C431 336 518 411 526 526L481 535C454 425 394 391 345 391C304 391 253 418 253 492C253 576 334 644 450 644C555 644 654 570 807 570C886 570 969 608 1025 657L999 699ZM718 558C656 515 608 467 525 323C414 275 334 215 298 179L333 143C356 162 405 196 473 228L469 220C413 111 343 34 239 34C194 34 170 50 159 65V66C199 73 217 105 217 134C217 169 193 201 149 201C102 201 65 158 65 108C65 32 126 -21 243 -21C396 -21 561 66 649 285C692 294 737 299 782 299C778 279 776 268 776 249C776 236 777 225 780 215L850 241C847 250 842 275 842 314C906 322 942 355 942 395C942 418 925 439 894 439C862 439 834 408 815 383C768 383 724 378 681 370C713 452 724 490 753 522L718 558Z" id="g199-7"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,51.37,15.969)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,56.93,15.969)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,64.08,22.233)"> <use 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xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,28.67,7.468)"> <use xlink:href="#g50-79"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.97,22.239)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,24.6,36.366)"> <use xlink:href="#g50-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,30.47,36.366)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,36.03,36.366)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.51,22.233)"> <use xlink:href="#g113-89"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.64,22.233)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.66,22.233)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.01,22.233)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,73.24,22.233)"> <use xlink:href="#g113-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,78.62,15.969)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,81.17,15.969)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,85.6,15.969)"> <use xlink:href="#g50-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,90.07,15.969)"> <use xlink:href="#g50-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,95.93,15.969)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,99.19,15.969)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,102.35,15.969)"> <use xlink:href="#g50-48"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,106.26,15.969)"> <use xlink:href="#g50-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,114.01,15.969)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,117.9,22.233)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="65.1429pt" id="I35" version="1.1" viewbox="0 0 147.55 65.1429" width="147.55pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -10.12)" xlink:href="#B35-1"></use> <use transform="matrix(1 0 0 1 26.58 24.94)" xlink:href="#B35-2"></use> </svg></span></span><span class="right_break" id="R35"> <svg class="label" height="11.44pt" id="M35-3" version="1.1" viewbox="0 0 21.478 11.44" width="21.478pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B35-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.54,9.26)"> <use xlink:href="#g190-227"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.98,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="65.1429pt" id="IL35" version="1.1" viewbox="0 0 21.56 65.1429" width="21.56pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 26.64)" xlink:href="#B35-3"></use> </svg></span></span>在哪里<我>t</我>= 1,2,…<我>N</我>。</p> <h5 id="sec3.3">3.3。ARFIMA模拟方法</h5> <p>我们使用了Matlab代码提出Fatichi [<一个href="#B14">14</一个>根据方程(),<一个href="#EEq12">12</一个>),在目前的情况下,我们有限的ARFIMA (0,<我>d</我>,0)模型,对方程(<一个href="#EEq13">13</一个>)。这段代码仅仅边界方程的总和(<一个href="#EEq15">15</一个>)<我>k</我>= 100。我们使用这个过程来生成fGn系列(<我>d</我>∈]−0.5,0.5 ()。为了获得所需的一整套系列,我们通过累积求和计算fBm系列。</p> <p>我们现在我们使用的三种评估方法。注意,为了更好的可读性,模拟系列的指数和表达的估计或转换<我>α</我>指标。估计标有一个长音符号(<span class="nowrap"> <svg height="9.4556pt" id="M36" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -9.24921 7.384 9.4556" width="7.384pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.227,-.222)"> <path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 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</svg>)。</span></p> <h5 id="sec3.4">3.4。去趋势波动分析</h5> <p>DFA算法如下所示,对于一个系列<我>x</我>(<我>t</我>)的长度<我>N</我>在哪里<我>t</我>= 1,2,…<我>N</我>。系列是第一个集成,通过计算<我>t</我>积累的离开意味着整个系列:<span class="equation_break" id="EEq27"><span class="left_break" id="L39"></span><span class="middle_break"><span class="center_break" id="M39"> <svg height="36.8735pt" id="M39-1" version="1.1" viewbox="0 0 112.844 36.8735" width="112.844pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B39-1"> <g transform="matrix(.013,0,0,-0.013,0,21.63)"> <use xlink:href="#g113-89"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.12,21.812)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.64,21.63)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.07,21.812)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.24,21.63)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,45.5,6.865)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.5,21.636)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,40.79,35.279)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,43.34,35.279)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,48.9,35.279)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,55.84,21.812)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,60.36,21.63)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.013,0,0,-0.013,69.81,21.812)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.32,21.63)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.87,21.812)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,85.3,21.63)"> <use 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</svg></span></span></p> <p>然后分为本系列集成<我>k</我>不重叠的时间间隔的长度<我>n</我>。最后一个<我>N</我><i>−</我><i>kn</我>数据点被排除在分析之外。在每个时间间隔内,最小二乘直线安装数据。该系列<我>X</我>(<我>t</我>减去)然后在本地去趋势的理论价值<我>X</我><sup>th</sup>(<我>t</我>)的回归。对于一个给定的区间长度<我>n</我>特点,本系列集成和去趋势波动的大小计算由以下方程:<span class="equation_break" id="EEq28"><span class="left_break" id="L40"></span><span class="middle_break"><span class="center_break" id="M40"> <svg height="45.4571pt" id="M40-1" version="1.1" viewbox="0 0 25.618 45.4571" width="25.618pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B40-1"> <g transform="matrix(.013,0,0,-0.013,0,28.246)"> <path d="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 575C302 609 304 615 338 615H426C502 615 517 604 526 581C534 560 536 524 537 492L565 494C574 554 583 631 584 650Z" id="g113-71"></path> </g> <g 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<p>在原始算法中,计算所有可能的时间间隔内重复长度,例如,从<我>n</我>= 10<我>n</我>=<我>N</我>/ 2 (<一个href="#B9">9</一个>]。在本文中,我们应用了<我>等间距的平均</我>版本的DFA (<一个href="#B29">29日</一个>),大大降低了估计的可变性。这个过程包括(日志)横坐标划分<我>P</我>箱子的长度<span class="inline_break"> <svg height="13.2658pt" id="M41" style="vertical-align:-3.97747pt" version="1.1" viewbox="-0.0498162 -9.28833 62.863 13.2658" width="62.863pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.498,0)"> <path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g121-106"></path> </g> <g transform="matrix(.013,0,0,-0.013,7.787,0)"> <use xlink:href="#g121-109"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.417,0)"> <path d="M463 437C426 431 375 425 327 422C297 440 264 449 231 449H230C153 449 51 396 51 283C51 215 94 168 139 149C123 129 91 103 51 88C50 78 53 60 62 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xlink:href="#g121-109"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.919,0)"> <use xlink:href="#g121-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,16.063,3.818)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.495,3.818)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.458,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.956,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,36.417,3.132)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,44.006,3.132)"> <use xlink:href="#g58-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,46.509,3.132)"> <use xlink:href="#g58-108"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.132,0)"> <use xlink:href="#g113-42"></use> </g> </svg>。</span>的<我>P</我>垃圾箱定义如下:<span class="equation_break" id="EEq29"><span class="left_break" id="L43"></span><span class="middle_break"><span class="center_break" id="M43"> <svg height="30.5685pt" id="M43-1" version="1.1" viewbox="0 0 37.025 30.5685" width="37.025pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B43-1"> <g transform="matrix(.013,0,0,-0.013,0,18.161)"> <path d="M152 404V712C115 698 54 683 7 677V654C71 648 73 642 73 579V24C128 -2 179 -12 220 -12C353 -12 471 92 471 238C471 357 381 449 274 449C262 449 249 446 233 439L152 404ZM152 374C170 384 202 393 230 393C313 393 382 326 382 213C382 97 330 26 246 26C194 26 165 62 158 81C154 91 152 101 152 116V374Z" id="g190-99"></path> </g> <g transform="matrix(.013,0,0,-0.013,6.44,18.161)"> <path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z" id="g190-106"></path> </g> <g transform="matrix(.013,0,0,-0.013,9.93,18.161)"> <use xlink:href="#g190-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,19.28,18.161)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.31,18.161)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.02,18.161)"> <use xlink:href="#g119-6"></use> </g> </g> </svg> <svg height="30.5685pt" id="M43-2" version="1.1" viewbox="0 0 78.035 30.5685" width="78.035pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B43-2"> <g transform="matrix(.013,0,0,-0.013,0,18.161)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.26,18.161)"> <path d="M417 -839V-790L351 -787C244 -783 242 -774 242 -668V1156C242 1314 245 1323 351 1327L417 1330V1379H170V-839H417Z" id="g119-153"></path> </g> <g transform="matrix(.013,0,0,-0.013,18.19,18.161)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.48,18.161)"> <use xlink:href="#g121-109"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.11,18.161)"> <use xlink:href="#g121-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,34.25,21.979)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.69,21.979)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.83,18.161)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.85,18.161)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,57.31,21.293)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,64.9,21.293)"> <use xlink:href="#g58-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,67.4,21.293)"> <use xlink:href="#g58-108"></use> </g> <g transform="matrix(.013,0,0,-0.013,73.03,18.161)"> <use xlink:href="#g119-6"></use> </g> </g> </svg> <svg height="30.5685pt" id="M43-3" version="1.1" viewbox="0 0 54.99 30.5685" width="54.99pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B43-3"> <g transform="matrix(.013,0,0,-0.013,0,18.161)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.54,18.161)"> <use xlink:href="#g119-149"></use> </g> <g transform="matrix(.013,0,0,-0.013,19.04,9.171)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.66,9.171)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.19,9.171)"> <use xlink:href="#g113-50"></use> </g> <rect height="0.65243" width="27.4719" x="19.04" y="14.508"></rect> <g transform="matrix(.013,0,0,-0.013,28.75,27.387)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.71,18.161)"> <use xlink:href="#g119-150"></use> </g> </g> </svg> <svg height="30.5685pt" id="M43-4" version="1.1" viewbox="0 0 2.964 30.5685" width="2.964pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B43-4"> <g transform="matrix(.013,0,0,-0.013,0,18.161)"> <use xlink:href="#g113-46"></use> </g> </g> </svg> <svg height="30.5685pt" id="M43-5" version="1.1" viewbox="0 0 90.514 30.5685" width="90.514pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B43-5"> <g transform="matrix(.013,0,0,-0.013,0,18.161)"> <use xlink:href="#g119-157"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.07,18.161)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.36,18.161)"> <use xlink:href="#g121-109"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.99,18.161)"> <use xlink:href="#g121-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,24.13,21.979)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,28.56,21.979)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,35.71,18.161)"> <use xlink:href="#g119-157"></use> </g> <g transform="matrix(.013,0,0,-0.013,44.96,9.305)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.43,12.436)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.99,12.436)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,63.07,12.436)"> <use xlink:href="#g58-118"></use> </g> <rect height="0.65243" width="23.0776" x="44.96" y="14.508"></rect> <g transform="matrix(.013,0,0,-0.013,45.4,27.387)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.86,30.519)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.45,30.519)"> <use xlink:href="#g58-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,61.96,30.519)"> <use xlink:href="#g58-108"></use> </g> <g transform="matrix(.013,0,0,-0.013,69.24,18.161)"> <use xlink:href="#g119-158"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.3,18.161)"> <use xlink:href="#g119-158"></use> </g> <g transform="matrix(.013,0,0,-0.013,87.55,18.161)"> <use xlink:href="#g113-60"></use> </g> </g> </svg> <svg height="30.5685pt" id="M43-6" version="1.1" viewbox="0 0 59.845 30.5685" width="59.845pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B43-6"> <g transform="matrix(.013,0,0,-0.013,0,18.161)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,3.29,18.161)"> <use xlink:href="#g121-109"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.92,18.161)"> <use xlink:href="#g121-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,16.06,21.979)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.49,21.979)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.64,18.161)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.66,18.161)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,39.12,21.293)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,46.71,21.293)"> <use xlink:href="#g58-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,49.21,21.293)"> <use xlink:href="#g58-108"></use> </g> <g transform="matrix(.013,0,0,-0.013,54.84,18.161)"> <use xlink:href="#g119-6"></use> </g> </g> </svg> <svg height="30.5685pt" id="M43-7" version="1.1" viewbox="0 0 120.664 30.5685" width="120.664pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B43-7"> <g transform="matrix(.013,0,0,-0.013,0,18.161)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.89,9.171)"> <use xlink:href="#g113-113"></use> </g> <rect height="0.65243" width="8.05108" x="11.73" y="14.508"></rect> <g transform="matrix(.013,0,0,-0.013,11.73,27.387)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.16,18.161)"> <use xlink:href="#g119-157"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.22,18.161)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.51,18.161)"> <use xlink:href="#g121-109"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.14,18.161)"> <use xlink:href="#g121-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,47.28,21.979)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.72,21.979)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.86,18.161)"> <use xlink:href="#g119-157"></use> </g> <g transform="matrix(.013,0,0,-0.013,68.12,9.305)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,74.58,12.436)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,82.14,12.436)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,86.23,12.436)"> <use xlink:href="#g58-118"></use> </g> <rect height="0.65243" width="23.0776" x="68.12" y="14.508"></rect> <g transform="matrix(.013,0,0,-0.013,68.56,27.387)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,75.02,30.519)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,82.61,30.519)"> <use xlink:href="#g58-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,85.11,30.519)"> <use xlink:href="#g58-108"></use> </g> <g transform="matrix(.013,0,0,-0.013,92.39,18.161)"> <use xlink:href="#g119-158"></use> </g> <g transform="matrix(.013,0,0,-0.013,100.45,18.161)"> <use xlink:href="#g119-158"></use> </g> <g transform="matrix(.013,0,0,-0.013,108.52,18.161)"> <path d="M361 -839V1379H114V1330L180 1327C286 1323 289 1314 289 1156V-668C289 -774 287 -783 180 -787L114 -790V-839H361Z" id="g119-154"></path> </g> <g transform="matrix(.013,0,0,-0.013,117.7,18.161)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="132.876pt" id="I43" version="1.1" viewbox="0 0 162.79 132.876" width="162.79pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B43-1"></use> <use transform="matrix(1 0 0 1 40.7 0)" xlink:href="#B43-2"></use> <use transform="matrix(1 0 0 1 12.87 39.43)" xlink:href="#B43-3"></use> <use transform="matrix(1 0 0 1 70.06 39.43)" xlink:href="#B43-5"></use> <use transform="matrix(1 0 0 1 12.14 71.3)" xlink:href="#B43-6"></use> <use transform="matrix(1 0 0 1 12.87 102.31)" xlink:href="#B43-7"></use> </svg></span></span><span class="right_break" id="R43"> <svg class="label" height="11.44pt" id="M43-8" version="1.1" viewbox="0 0 21.388 11.44" width="21.388pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B43-8"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.54,9.26)"> <use xlink:href="#g190-193"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.89,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="132.876pt" id="IL43" version="1.1" viewbox="0 0 21.47 132.876" width="21.47pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 60.51)" xlink:href="#B43-8"></use> </svg></span></span>在哪里<我>p</我>= 1,2,…<我>P</我>。在目前的分析,我们组<我>n</我><sub>最小值</sub>= 10,<我>n</我><sub>马克斯</sub>= 512,<我>P</我>= 18。</p> <p>在每一个本<span class="nowrap"> <svg height="10.2124pt" id="M44" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 7.83752 10.2124" width="7.83752pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-113"></use> </g> </svg>,</span>平均时间间隔长度<svg height="12.7178pt" id="M45" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 23.4177 12.7178" width="23.4177pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <rect height="0.65243" width="6.55046" x="0" y="-8.52081"></rect> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,6.55,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.048,0)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.759,0)"> <use xlink:href="#g113-42"></use> </g> </svg>和平均波动的大小<svg height="15.3275pt" id="M46" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.8981 40.368 15.3275" width="40.368pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <rect height="0.65243" width="7.92058" x="0" y="-11.1958"></rect> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.921,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.419,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.945,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.443,0)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.153,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,35.651,0)"> <use xlink:href="#g113-42"></use> </g> </svg>计算。预计一个幂律<span class="equation_break" id="EEq30"><span class="left_break" id="L47"></span><span class="middle_break"><span class="center_break" id="M47"> <svg height="15.8625pt" id="M47-1" version="1.1" viewbox="0 0 112.194 15.8625" width="112.194pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B47-1"> <rect height="0.65243" width="7.92058" x="0" y=".702"></rect> <g transform="matrix(.013,0,0,-0.013,0,11.898)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.1,11.898)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.12,11.898)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.83,11.898)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.85,11.898)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.013,0,0,-0.013,36.56,11.898)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.61,11.898)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.29,11.898)"> <use xlink:href="#g113-29"></use> </g> <g transform="matrix(.013,0,0,-0.013,64.67,11.898)"> <use xlink:href="#g119-5"></use> </g> <rect height="0.65243" width="6.55046" x="69.7" y="3.377"></rect> <g transform="matrix(.013,0,0,-0.013,69.7,11.898)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,78.43,11.898)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,83.45,11.898)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.013,0,0,-0.013,91.16,11.898)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,96.21,11.898)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,101.24,4.597)"> <path d="M558 106L533 129C501 84 476 67 464 67C446 67 435 116 414 239C457 297 508 367 550 440L539 451L484 438C458 390 429 338 404 300H402C375 407 351 451 285 451C168 451 24 312 24 153C24 56 66 -12 132 -12C206 -12 284 64 345 156H347C367 24 386 -12 422 -12C457 -12 503 7 558 106ZM338 206C272 99 215 56 173 56C140 56 116 96 116 170C116 303 194 405 255 405C304 405 324 299 338 206Z" id="g50-223"></path> </g> <g transform="matrix(.013,0,0,-0.013,109.23,11.898)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R47"> <svg class="label" height="11.44pt" id="M47-2" version="1.1" viewbox="0 0 21.438 11.44" width="21.438pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B47-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.53,9.26)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.94,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>指数估计(<span class="nowrap"> <svg height="9.4556pt" id="M48" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -9.24921 7.384 9.4556" width="7.384pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.227,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-223"></use> </g> </svg>)</span>得到的双对数图的斜率<svg height="15.3275pt" id="M49" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.8981 40.368 15.3275" width="40.368pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <rect height="0.65243" width="7.92058" x="0" y="-11.1958"></rect> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.921,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.419,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.945,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.443,0)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.153,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,35.651,0)"> <use xlink:href="#g113-42"></use> </g> </svg>的函数<span class="nowrap"> <svg height="12.7178pt" id="M50" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 23.4177 12.7178" width="23.4177pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <rect height="0.65243" width="6.55046" x="0" y="-8.52081"></rect> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,6.55,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.048,0)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.759,0)"> <use xlink:href="#g113-42"></use> </g> </svg>。</span></p> <h5 id="sec3.5">3.5。功率谱密度(PSD)进行分析</h5> <p>这个方法工作的基础上获得的周期图的快速傅里叶变换算法和利用的幂律方程(<一个href="#EEq8">8</一个>)。<svg height="16.0061pt" id="M51" style="vertical-align:-3.4295pt" version="1.1" viewbox="-0.0498162 -12.5766 8.465 16.0061" width="8.465pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,2.355,-3.549)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-224"></use> </g> </svg>预计通过计算负斜率(−吗<我>β</我>日志(相关的)的行<我>年代</我>(<我>f</我>)记录<我>f</我>。</p> <p>在本文中,我们使用提出的改进版本馥香(<一个href="#B30">30.</一个>)通过补充和修改等。<一个href="#B10">10</一个>),被指定为<sup>低</sup>PSD<sub>我们</sub>。这种方法使用的组合预处理操作:首先,系列中减去从每个值的均值,然后一个抛物线窗口是applied-each系列的价值乘以下列功能:<span class="equation_break" id="EEq31"><span class="left_break" id="L52"></span><span class="middle_break"><span class="center_break" id="M52"> <svg height="44.8047pt" id="M52-1" version="1.1" viewbox="0 0 155.494 44.8047" width="155.494pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B52-1"> <g transform="matrix(.013,0,0,-0.013,0,15.095)"> <path d="M660 1109V1150C557 1150 406 1122 406 886V0H513V923C513 1011 529 1089 660 1109Z" id="g119-47"></path> </g> <g transform="matrix(.013,0,0,-0.013,0,30.232)"> <path d="M513 0V380C513 490 473 586 374 614V618C474 644 513 740 513 848V1200H406V816C406 746 399 654 186 642V590C399 578 406 486 406 416V0H513Z" id="g119-63"></path> </g> <g transform="matrix(.013,0,0,-0.013,0,44.755)"> <path d="M660 33V74C529 94 513 176 513 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xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B52-1"></use> </svg></span></span><span class="right_break" id="R52"> <svg class="label" height="11.44pt" id="M52-2" version="1.1" viewbox="0 0 19.078 11.44" width="19.078pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B52-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.19,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.58,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="44.8047pt" id="IL52" version="1.1" viewbox="0 0 19.16 44.8047" width="19.16pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 16.47)" xlink:href="#B52-2"></use> </svg></span></span>在哪里<我>t</我>= 1,2,…<我>N</我>。</p> <p>其次,消除长期趋势的桥梁是由减去从数据线路连接的第一个和最后一个点系列:<span class="equation_break" id="EEq32"><span class="left_break" id="L53"></span><span class="middle_break"><span class="center_break" id="M53"> <svg height="45.4798pt" id="M53-1" version="1.1" viewbox="0 0 240.674 45.4798" width="240.674pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B53-1"> <g transform="matrix(.013,0,0,-0.013,0,15.433)"> <use xlink:href="#g119-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,30.569)"> <use xlink:href="#g119-63"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,45.092)"> <use xlink:href="#g119-71"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.72,20.093)"> <path d="M238 681C243 705 239 712 230 712C217 712 156 682 75 674L70 648H105C148 648 153 641 144 598L39 110C18 11 35 -12 55 -12C90 -12 166 36 221 103L205 125C174 93 130 65 118 65C112 65 108 68 114 96L238 681Z" 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transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.16,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.21,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="45.4798pt" id="IL53" version="1.1" viewbox="0 0 20.79 45.4798" width="20.79pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 16.81)" xlink:href="#B53-2"></use> </svg></span></span>在哪里<我>t</我>= 1,2,…<我>N</我>。</p> <p>傅里叶变换应用于修改后的系列<span class="nowrap"> <svg height="10.3116pt" id="M54" style="vertical-align:-4.35069pt" version="1.1" viewbox="-0.0498162 -5.96091 19.0617 10.3116" width="19.0617pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-120"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.773,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.93,3.132)"> <use xlink:href="#g50-109"></use> </g> </svg>,</span>的拟合<我>β</我>排除了高频功率估计(<我>f</我>>最大频率的1/8)。这个方法被证明补充et al。<一个href="#B10">10</一个>)提供更可靠的估计谱指数。允许直接对比方法,<我>β</我>然后转换成<我>α</我>指标通过一个简单的线性变换<span class="inline_break"> <svg height="16.0061pt" id="M55" style="vertical-align:-3.4295pt" version="1.1" viewbox="-0.0498162 -12.5766 23.173 16.0061" width="23.173pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,5.725,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.498,0)"> <use xlink:href="#g113-223"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.542,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span> <svg height="16.0061pt" style="vertical-align:-3.4295pt" version="1.1" viewbox="26.7541838 -12.5766 22.616 16.0061" width="22.616pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,26.804,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.658,-3.549)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.302,0)"> <use xlink:href="#g113-224"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.789,0)"> <use xlink:href="#g117-36"></use> </g> </svg><span class="ibiop"></span> <svg height="16.0061pt" style="vertical-align:-3.4295pt" version="1.1" viewbox="52.2761838 -12.5766 16.094 16.0061" width="16.094pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,52.326,0)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.566,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.064,0)"> <use xlink:href="#g113-48"></use> </g> </svg><span class="isep"></span><span class="nowrap"> <svg height="16.0061pt" style="vertical-align:-3.4295pt" version="1.1" viewbox="68.3751838 -12.5766 10.738 16.0061" width="10.738pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,68.425,0)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.665,0)"> <use xlink:href="#g113-42"></use> </g> </svg>。</span></span></p> <h5 id="sec3.6">3.6。ARFIMA模型</h5> <p>的<我>d</我>参数估计通过拟合ARFIMA (0,<我>d</我>,0)模型系列使用惠特尔近似极大似然估计量。我们使用了ARFIMA (<我>p</我>,<我>d</我>,<我>问</我>)估计方案提出的Matlab Inzelt [<一个href="#B31">31日</一个>在Matlab中央文件交换平台。</p> <p>正如前面解释的,只有fGn系列和ARFIMA模型持有<我>d</我>有界区间内)−0.5,0.5 (。fBm系列、Diebolt和Guiraud [<一个href="#B32">32</一个>]提出ARFIMA模型应用于相应的fGn(分化得到的),然后估计的理论部分参数通过添加1 fBm系列<我>d</我>从fGn获得价值。然而,这种策略需要一个先验评估fGn / fBm分类系列。一些解决方案,基于方法的初步应用工作漠不关心地fGn fBm,如DFA或PSD已经提出,但产生了重要的百分比在1 /误分类<我>f</我>边界(<一个href="#B9">9</一个>,<一个href="#B10">10</一个>]。</p> <p>为了应用ARFIMA模型地fGn和fBm系列,DFA和PSD,我们使用以下策略:该算法包含在寻找最好的惠特尔近似极大似然估计量的约束优化。根据ARFIMA属性,输出参数是有界的,产生参数值<svg height="12.783pt" id="M56" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -12.5766 56.303 12.783" width="56.303pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,2.708,-3.549)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.874,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.137,0)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.377,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.341,0)"> <path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 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<use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"> <use xlink:href="#g190-112"></use> </g> </svg>,</span>从最初的系列,等于0.4999,该系列被认为是fBm分化和算法应用于时间序列来获得<svg height="15.8495pt" id="M58" style="vertical-align:-3.2729pt" version="1.1" viewbox="-0.0498162 -12.5766 19.499 15.8495" width="19.499pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,2.708,-3.549)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"> <use xlink:href="#g190-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.955,3.132)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.394,3.132)"> <path d="M99 437H52L25 408L28 397H99V104C99 38 91 32 32 26V0H246V25C185 32 178 38 178 104V397H365V104C365 38 358 32 303 25V0H526V25C451 32 444 37 444 104V397H555C565 404 568 428 563 437H444V471C443 562 453 609 466 629C476 647 492 661 518 661C551 661 581 639 600 620C609 611 619 612 629 620C637 626 647 636 650 644C654 654 654 666 645 677C627 697 597 710 564 712C521 707 476 686 432 642C412 664 374 688 316 690C269 685 230 668 190 636C139 596 120 551 111 525C104 505 99 477 99 449V437ZM365 437H178V461C178 537 192 580 209 605C223 627 245 648 283 648C336 648 374 615 394 585C384 566 378 550 374 533C369 516 365 488 365 456V437Z" id="g190-155"></path> </g> </svg>估计。在这个不稳定的情况下,<svg height="15.8495pt" id="M59" style="vertical-align:-3.2729pt" version="1.1" viewbox="-0.0498162 -12.5766 61.889 15.8495" width="61.889pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,2.708,-3.549)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-101"></use> </g> <g 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transform="matrix(.013,0,0,-0.013,2.708,-3.549)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.874,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.844,-3.549)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.137,0)"> <use xlink:href="#g113-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,29.287,3.132)"> <use xlink:href="#g190-112"></use> </g> </svg>。</span>这个参数估计<svg height="12.783pt" id="M61" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -12.5766 8.818 12.783" width="8.818pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,2.708,-3.549)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-101"></use> </g> </svg>然后转换成<我>α</我>指标通过一个简单的线性变换<span class="inline_break"> <svg height="14.8447pt" id="M62" style="vertical-align:-2.2681pt" version="1.1" viewbox="-0.0498162 -12.5766 23.173 14.8447" width="23.173pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,5.725,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.498,0)"> <use xlink:href="#g113-223"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.542,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span> <svg height="14.8447pt" style="vertical-align:-2.2681pt" version="1.1" viewbox="26.7541838 -12.5766 28.517 14.8447" width="28.517pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,26.804,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.302,0)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.25,-3.549)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.542,0)"> <use xlink:href="#g113-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.69,0)"> <use xlink:href="#g117-36"></use> </g> </svg><span class="ibiop"></span> <svg height="14.8447pt" style="vertical-align:-2.2681pt" version="1.1" viewbox="58.1761838 -12.5766 16.094 14.8447" width="16.094pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,58.226,0)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,64.466,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,68.964,0)"> <use xlink:href="#g113-48"></use> </g> </svg><span class="isep"></span><span class="nowrap"> <svg height="14.8447pt" style="vertical-align:-2.2681pt" version="1.1" viewbox="74.2761838 -12.5766 10.738 14.8447" width="10.738pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,74.326,0)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.566,0)"> <use xlink:href="#g113-42"></use> </g> </svg>。</span></span></p> <h4 id="results">4所示。结果</h4> <p>我们现在在图<一个href="//www.newsama.com/journals/cmmm/2019/4025305/fig1/" target="_blank">1</一个>真正的之间的关系<我>α</我>和的意思<svg height="9.4556pt" id="M63" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -9.24921 7.384 9.4556" width="7.384pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.227,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-223"></use> </g> </svg>值,为每个模拟和估算方法。如果我们考虑全球标识线形状的结果,很明显,估计方法生成的系列时表现的更好方法属于同一个域(见沿着下行对角线三个图表等)。这是已经观察到勉强et al。<一个href="#B11">11</一个>]。</p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="" name="4025305.fig.001" src="https://static-01.hindawi.com/articles/cmmm/volume-2019/4025305/figures/4025305.fig.001.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cmmm/2019/4025305/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 真正的和平均估计之间的关系<我>α</我>值。上面一行:DH算法生成的系列;由导弹生成的中间行:系列;底下一行:ARFIMA模拟生成的系列。左栏:估计与DFA执行;中心柱:估计与PSD执行;右列:估计与ARFIMA模型。虚线代表的身份。</d我v> </div> </div> </div> <p>第一行描述了三种估计方法的结果与系列DH生成的算法。常见的偏差出现在三个图形,强烈的低估<我>α</我>在fBm系列中,接近1 /<我>f</我>边界。这揭示了一个明确的破坏原始fGn / fBm模型。这种现象时没有被观察到系列与其他两个方法生成。</p> <p>DFA倾向于低估<我>α</我>fBm系列,尤其是系列被地对地导弹或ARFIMA建模与生成。相反,PSD倾向于高估<我>α</我>fBm系列,尤其是系列被ARFIMA DH算法或生成的建模。</p> <p>图<一个href="//www.newsama.com/journals/cmmm/2019/4025305/fig2/" target="_blank">2</一个>代表一个焦点在1 /以前的结果<我>f</我>边界(即。,从<我>α</我>= 0.9<我>α</我>= 1.1)。第一行证实了明显的中断,在1 /<我>f</我>边界,对DH系列生成算法。此外,它揭示了一个轻微高估fGn系列,附近的1 /<我>f</我>噪音,对PSD和ARFIMA模型。相比之下,所产生的系列导弹和ARFIMA模拟1 /呈现一个清晰的连续性<我>f</我>边界,任何估算的方法。DFA倾向于高估<我>α</我>系列光谱产生的合成,但不是与ARFIMA系列模拟。PSD倾向于高估<我>α</我>在这个特定的范围。最后,ARFIMA模型稍微高估了<我>α</我>fBm系列由SSM。</p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig2"> <div class="floats-partial-content fig-content-fig2"> <div class="partial-carousel--single-image"> <img alt="" name="4025305.fig.002" src="https://static-01.hindawi.com/articles/cmmm/volume-2019/4025305/figures/4025305.fig.002.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cmmm/2019/4025305/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 真正的和平均估计之间的关系<我>α</我>值,重点是1 /<我>f</我>边界(≤0.9<我>α</我>≥1.1)。上面一行:DH算法生成的系列;由导弹生成的中间行:系列;底下一行:ARFIMA模拟生成的系列。左栏:估计与DFA执行;中心柱:估计与PSD执行;右列:估计与ARFIMA模型。虚线代表的身份。</d我v> </div> </div> </div> <p>最后,我们呈现在图<一个href="//www.newsama.com/journals/cmmm/2019/4025305/fig3/" target="_blank">3</一个>的可变性(标准差)<svg height="9.4556pt" id="M64" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -9.24921 7.384 9.4556" width="7.384pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.227,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-223"></use> </g> </svg>样本,为每个模拟和估算方法。这些图表给出了具有相同规模的垂直斧,为了方便对比方法。在全球范围内,<svg height="9.4556pt" id="M65" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -9.24921 7.384 9.4556" width="7.384pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.227,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-223"></use> </g> </svg>似乎少了DH算法生成的变量串联或ARFIMA模拟,比那些来自导弹、产生了最糟糕的结果。关于评估方法,DFA结果显示明显增加<svg height="9.4556pt" id="M66" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -9.24921 7.384 9.4556" width="7.384pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.227,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-223"></use> </g> </svg>变异性是真实的<我>α</我>增加。这种效应与PSD和ARFIMA模型不存在,在变化保持稳定对整个事实<我>α</我>的范围内。PSD的结果揭示了高水平的变化,特别是当系列是由导弹。相反,ARFIMA模型的特点是低变异性。</p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig3"> <div class="floats-partial-content fig-content-fig3"> <div class="partial-carousel--single-image"> <img alt="" name="4025305.fig.003" src="https://static-01.hindawi.com/articles/cmmm/volume-2019/4025305/figures/4025305.fig.003.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cmmm/2019/4025305/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 真正的关系<我>α</我>和估计的可变性<我>α</我>值(标准差)。上面一行:DH算法生成的系列;由导弹生成的中间行:系列;底下一行:ARFIMA模拟生成的系列。左栏:估计与DFA执行;中心柱:估计与PSD执行;右列:估计与ARFIMA模型。</d我v> </div> </div> </div> <h4 id="discussion">5。讨论</h4> <h5 id="sec5.1">5.1。Davies-Harte算法</h5> <p>最重要的观察与DH算法生成的系列的强烈偏见fBm系列接近1 /<我>f</我>边界。这个结果,一致获得三种分析方法,显然应该归因于偏见的一代技术。Stadnitski(这个结果已经证明了这一点<一个href="#B27">27</一个>),他认为“观察到的差异可能是由于无能Davies-Harte技术提供fBm系列<我>H</我>接近0。这些结果强调的重要性,一个适当的数据生成模拟研究和修订的结果研究表明采用Davies-Harte技术”(页144还是145)。</p> <p>Delignieres [<一个href="#B28">28</一个>]表明,这种偏见并不是Davies-Harte相关算法,但更重要的是fGn / fBm模型本身。基于模型的前提,尤其是fGn的自相关(方程(<一个href="#EEq5">5</一个>)),作者推导的解析表达式fBm的自相关:<span class="equation_break" id="EEq33"><span class="left_break" id="L67"></span><span class="middle_break"><span class="center_break" id="M67"> <svg height="35.5583pt" id="M67-1" version="1.1" viewbox="0 0 39.618 35.5583" width="39.618pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B67-1"> <g transform="matrix(.013,0,0,-0.013,0,20.282)"> <path d="M516 277C516 378 460 448 376 448C335 448 288 434 240 401C158 345 127 277 107 159C53 -161 38 -221 23 -247L28 -261C43 -260 95 -250 114 -226C122 -216 129 -199 146 -75C152 -29 157 0 164 31C182 9 206 -12 237 -12C267 -12 325 8 376 46C451 102 516 179 516 277ZM432 259C432 134 366 40 259 40C236 40 204 48 171 76L195 203C219 327 253 400 326 400C398 400 432 336 432 259Z" id="g113-239"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,6.17,23.414)"> <use 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transform="matrix(.013,0,0,-0.013,80.2,31.615)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.013,0,0,-0.013,94.02,31.615)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,104.56,31.615)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,108.99,31.797)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,115.77,31.615)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,120.2,27.439)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,124.63,27.439)"> <use xlink:href="#g50-73"></use> </g> <g transform="matrix(.013,0,0,-0.013,132.88,31.615)"> <path d="M244 -259V799H63V768H72C178 759 181 755 181 616V-109C181 -215 179 -219 72 -228H63V-259H244Z" id="g119-2"></path> </g> <g transform="matrix(.013,0,0,-0.013,138.97,20.282)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="57.5734pt" id="I67" version="1.1" viewbox="0 0 155.62 57.5734" width="155.62pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -11.1)" xlink:href="#B67-1"></use> <use transform="matrix(1 0 0 1 13.6 22.01)" xlink:href="#B67-2"></use> </svg></span></span><span class="right_break" id="R67"> <svg class="label" height="11.44pt" id="M67-3" version="1.1" viewbox="0 0 20.558 11.44" width="20.558pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B67-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.18,9.26)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.06,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="57.5734pt" id="IL67" version="1.1" viewbox="0 0 20.64 57.5734" width="20.64pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 22.86)" xlink:href="#B67-3"></use> </svg></span></span>在哪里<我>N</我>是系列的长度。我们报告在图<一个href="//www.newsama.com/journals/cmmm/2019/4025305/fig4/" target="_blank">4</一个>理论lag-1自我,计算fGn系列等<我>H</我>根据方程(= 0到1<一个href="#EEq5">5</一个>)和fBm系列等<我>H</我>根据方程(= 0到1<一个href="#EEq33">33</一个>),考虑<我>N</我>= 1024。这些结果证据严重故障的相关性属性的系列fGn / fBm边界,fBm的极限行为,<我>H</我>接近0,是不相关的白噪声。</p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig4"> <div class="floats-partial-content fig-content-fig4"> <div class="partial-carousel--single-image"> <img alt="" name="4025305.fig.004" src="https://static-01.hindawi.com/articles/cmmm/volume-2019/4025305/figures/4025305.fig.004.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cmmm/2019/4025305/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 理论lag-1相关fGn (a),基于方程(<一个href="#EEq5">5</一个>fBm)和(b),基于方程(<一个href="#EEq33">33</一个>),<我>α</我>值从0到2(改编自Delignieres [<一个href="#B28">28</一个>])。</d我v> </div> </div> </div> <p>这表明fBm系列,获得相应的累积求和fGn系列,事实上应该fGn非常低<我>H</我>值。根据方程(<一个href="#EEq33">33</一个>),我们计算的预期<svg height="12.7178pt" id="M68" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 37.5583 12.7178" width="37.5583pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-239"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.162,3.132)"> <use xlink:href="#g190-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.856,3.132)"> <use xlink:href="#g190-67"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.133,3.132)"> <use xlink:href="#g190-110"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.142,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.64,0)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.88,0)"> <use xlink:href="#g113-42"></use> </g> </svg>值,<我>H</我>从0.01到0.1,而这些预期值意味着lag-1自我观察与Davies-Harte系列的模拟算法。结果见图<一个href="//www.newsama.com/journals/cmmm/2019/4025305/fig5/" target="_blank">5</一个>和显示模拟的相关结构系列匹配密切的预期fGn / fBm模型。</p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig5"> <div class="floats-partial-content fig-content-fig5"> <div class="partial-carousel--single-image"> <img alt="" name="4025305.fig.005" src="https://static-01.hindawi.com/articles/cmmm/volume-2019/4025305/figures/4025305.fig.005.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cmmm/2019/4025305/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 预期,观察lag-1 fBm信号自相关。实线:理论lag-1 fBm信号的自相关,<我>H</我>从0.01到0.1,计算方程的基础上(<一个href="#EEq33">33</一个>)。白圈:意味着lag-1自我观察与Davies-Harte系列的模拟算法。</d我v> </div> </div> </div> <h5 id="sec5.2">5.2。谱合成方法</h5> <p>与DH算法相比,导弹在1 /提供连续性<我>f</我>边界。这种连续性预计,导弹在整个范围的地工作<我>β</我>指数。这个结果可能是奇怪的,因为fGn / fBm和光谱模型通常被认为是等价的,代表类似的属性在时间和频率域,分别。</p> <p>另一个重要的结果是相关的可变性估计,它系统地串联由SSM高于观察与其他的生成方法。这种方法,这是一个重要的问题似乎无法提供系列充分接近预期指数。</p> <h5 id="sec5.3">5.3。ARFIMA模拟</h5> <p>ARFIMA模拟1 /还提供了一个不错的连续性<我>f</我>边界。这个结果很有趣,fBm系列是在这种情况下得到的累积求和fGn的记者,至于DH算法。此外,获得套系列提出了最低的变异性指数估计,无论使用方法。这些结果表明,我们可以得到一个好的信心ARFIMA生成的系列,与其他两个方法。</p> <h5 id="sec5.4">5.4。去趋势波动分析</h5> <p>DFA与fGn系列很好,但工作提出了一个系统的负偏压和fBm系列的高水平的变化。对于理解这些可怜的结果与fBm系列,与其他方法相比,重要的是要记住,DFA确实有效集成系列,在这种情况下fBm集成。这个家庭overdiffusive过程并不清楚,和扩散财产利用DFA似乎适度适当等系列(<一个href="#B9">9</一个>]。</p> <p>DFA是一个非常受欢迎的方法,提出了优势地适用于fGn和fBm。其他一些方法给了令人满意的结果,但只有fGn相关(例如,dispersional分析或新范围分析(<一个href="#B33">33</一个>fBm])或(例如,缩放窗口的方差分析(<一个href="#B34">34</一个>])。然而,研究人员往往无法知道他们的信号指的是任何一个家庭,尤其是如果这些信号是接近1 /<我>f</我>边界。DFA可以克服这个问题。DFA的糟糕表现fBm信号可以被忽视的,考虑到大多数生理系列落入fGn的家庭。然而,在某些情况下,例如,姿势摇摆或目光波动,系列显然是不稳定的,应该视为fBm。在这种情况下,可以考虑运用DFA差系列或省略的整合步骤算法(见,例如,<一个href="#B35">35</一个>,<一个href="#B36">36</一个>])。</p> <p>值得注意的是,目前的结果与DFA的等间距的版本,这是证明显著改善的准确性和减少可变性原来的方法(<一个href="#B29">29日</一个>]。与原算法的结果会更糟。</p> <h5 id="sec5.5">5.5。功率谱密度</h5> <p>尽管提出的改进的应用补充et al。<一个href="#B10">10</一个>),PSD提供最坏的估计结果。的准确性,PSD倾向于高估<我>α</我>fBm系列,结果尤其欺骗性的可变性。PSD仍然是一个非常受欢迎的方法,特别是因为它提供了吸引人的图形结果。外的双对数功率谱表示,估计1 /<我>f</我>斜率,可以给重要迹象的存在和短期波动的本质系列(见,例如,<一个href="#B37">37</一个>,<一个href="#B38">38</一个>])。然而,对于指数评估的特定目的,PSD似乎明显优于其他方法。</p> <h5 id="sec5.6">5.6。ARFIMA模型</h5> <p>ARFIMA模型忽视了大多数以前的研究比较分形方法(<一个href="#B9">9</一个>- - - - - -<一个href="#B11">11</一个>]。Rangarajan周二和丁<一个href="#B39">39</一个>)开发了一个分形分析的综合方法将新范围和光谱分析,但他们从未考虑过ARFIMA作为一个可能的替代或补充。然而,这种方法提供了最准确的和不变量估计。介绍,表明ARFIMA模型最初是专为占固定系列。Diebolt提出和Guiraud [<一个href="#B32">32</一个>),我们有区别的非平稳系列ARFIMA模型的应用之前,这方法给了令人满意的结果。我们应用一个非常简单的程序区别平稳和非平稳的系列,考虑到系列屈服<我>d</我>估计等于上限与算法(0.49999)应该考虑获得的非平稳。这个简单的程序提供了良好的结果,就是明证的连续性观察到1 /<我>f</我>边界。在这个工作的初始步骤,我们测试了ARFIMA包(<一个href="#B40">40</一个>,<一个href="#B41">41</一个>牛)的矩阵计算语言<一个href="#B42">42</一个>]。然而,这种算法1 /给了更糟糕的结果<我>f</我>边界。刘等人。<一个href="#B43">43</一个>)最近提议的第一评价多样化ARFIMA程序,可用在各种平台上(Matlab,<我>R</我>、SAS和OxMetrics),提供解决方案模拟、参数估计和预测。进一步的调查应提供有效的指导方针所需的选择最相关的解决方案。</p> <p>在本文中,我们限制自己的估计ARFIMA (0,<我>d</我>,0)模型。ARFIMA模型也可以占各种自回归和/或移动平均过程可能污染实证系列。这种方法允许隔离在系列远程相关性,然后提供一个更好的估计分形指数。最后,程序使用ARFIMA模型提出了衡量真正的有效存在长期相关性实证系列(<一个href="#B26">26</一个>,<一个href="#B38">38</一个>,<一个href="#B44">44</一个>]。事实上,短期过程可能有时模仿1 /<我>f</我>例如波动,产生的错误检测远程相关性等经典方法DFA (<一个href="#B38">38</一个>]。托瑞等人提出的方法。<一个href="#B26">26</一个>)允许测试的相对可能性各种ARMA和ARFIMA模型,最后得出结论的有效存在长期相关性。</p> <p>为了说明实验有效性的这些结果,我们三个评估方法应用于一组系列的步伐持续时间,15分钟步行期间收集的发作与两组参与者:第一个是由22个年轻的参与者(28.07岁±8.88)和第二个23的老年人(72.36岁±4.88)。最近的实验中所收集的这些数据都表现在我们的实验室<一个href="#B45">45</一个>,<一个href="#B46">46</一个>),每个系列有一个长度为512数据点。正如前面指出,豪斯多夫等。<一个href="#B47">47</一个>]表明,老化的特征是一个典型的损失行走动力学的复杂性,和一个有望显著差异的证据<我>α</我>估计在两组之间。我们在表<一个href="//www.newsama.com/journals/cmmm/2019/4025305/tab1/" target="_blank">1</一个>与三种方法获得的结果,在转换<我>α</我>比较的指标。按照我们之前的结果,PSD产生了更大的变化估计比DFA或ARFIMA。我们与单向方差分析比较了两个样品,没有证据表明两组之间的任何差异的基础上PSD的估计。相比之下,DFA的显著差异被发现,ARFIMA估计,ARFIMA更强大的效果。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-content fig-content-tab1"> <table class="table-group" id="tab1"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="5"> <hr></td> </tr> <tr class="thead"> <td class="align_center" colspan="2"></td> <td class="align_center">DFA</td> <td class="align_center">PSD</td> <td class="align_center">ARFIMA</td> </tr> <tr> <td class="thead-hr" colspan="5"> <hr></td> </tr> <tr> <td class="align_center">年轻的</td> <td class="align_center">意思是(<我>α</我>DFA) SD</td> <td class="align_center">0.878 (0.096)</td> <td class="align_center">1.023 (0.137)</td> <td class="align_center">0.887 (0.096)</td> </tr> <tr> <td class="align_center">上了年纪的</td> <td class="align_center">意思是(<我>α</我>DFA) SD</td> <td class="align_center">0.783 (0.112)</td> <td class="align_center">0.951 (0.196)</td> <td class="align_center">0.764 (0.088)</td> </tr> <tr> <td class="align_left" rowspan="3"></td> <td class="align_center"><i>F</我>(43)</td> <td class="align_center">9.397</td> <td class="align_center">1.999</td> <td class="align_center">20.044</td> </tr> <tr> <td class="align_center"><span style="width: 7.83752ptpx;"> <svg height="10.2124pt" id="M69" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 7.83752 10.2124" width="7.83752pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path> </g> </svg></span></td> <td class="align_center">0.004</td> <td class="align_center">0.165</td> <td class="align_center">0.000</td> </tr> <tr> <td class="align_center">部分<我>η</我><sup>2</sup></td> <td class="align_center">0.179</td> <td class="align_center">0.044</td> <td class="align_center">0.318</td> </tr> <tr class="table-tr"> <td colspan="5"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cmmm/2019/4025305/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 的意思是<我>α</我>(在括号标准差)估计,计算的三种方法(DFA, PSD, ARFIMA),从跨步时间系列的系列,15分钟步行期间收集的发作与年轻(<我>N</我>= 22)及以上(<我>N</我>= 23)的参与者。</d我v> </div> </div> </div> <p>ARFIMA模型的优越性,超出了我们的见解的准确性和多样性指数估计的精确合成信号,这最终结果显示ARFIMA模型提供了一个更好的统计力量比DFA或PSD的实验数据分析<一个href="#B48">48</一个>]。进一步的调查仍有必要,然而,评估这些方法各自的性能,尤其是在更短的时间序列,它代表了一个重要的挑战人类行为实验(<一个href="#B9">9</一个>- - - - - -<一个href="#B12">12</一个>,<一个href="#B21">21</一个>,<一个href="#B29">29日</一个>,<一个href="#B49">49</一个>]。</p> <h4 id="conclusion">6。结论</h4> <p>本研究为ARFIMA方法的使用提供了一个强有力的支持,为模拟以及参数估计的目的。正如前面指出的,ARFIMA方法没有考虑最近实证比较研究,很少利用的作品,至少在生理和行为领域。的准确性和低变异性指数估计ARFIMA模型应该说服他们的优势,这种方法,特别是对于检测意味着组之间的差异。这种方法应该吸引研究人员的注意,为他们的未来实验或回顾以前的结果。</p> <h4 id="data-availability">数据可用性</h4> <p>时间序列用于支持本研究的发现可以从相应的作者。</p> <h4 id="disclosure">信息披露</h4> <p>这项工作已经部分作为海报在463年第13届会议的博士学校“人体运动科学”蒙彼利埃,6月2日,2017年,在第17届国际大会在体育活动和运动协会的研究(acap),第戎,2017年10月29日到31日。</p> <h4 id="conflicts-of-interest">的利益冲突</h4> <p>作者声明,这项研究是在没有进行任何商业或财务关系可能被视为潜在的利益冲突。</p> <h4 id="acknowledgments">确认</h4> <p>这项工作是支持的大学Montpellier-France(批准号busr - 2014)。作者感谢博士Zainy M.H. Almurad提供表5中使用的数据。</p> </div> <div class="xml-content"> <h4 class="references" id="references">引用</h4> <ol> <li id="B1">d . Gilden t·桑顿,m -马龙,“1 /<我>f</我>噪声在人类认知。”<我>科学</我>,卷267,不。5205年,第1839 - 1837页,1995年。<span class="reflinks">视图:<一个href="https://doi.org/10.1126/science.7892611">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=1/f%20noise%20in%20human%20cognition&author=D. Gilden&author=T. Thornton&author=&author=M. Mallon&publication_year=1995" target="_blank">谷歌学术搜索</一个></span></li> <li id="B2">j·m·豪斯多夫·c·k·彭,z拉登,j . y . Wei和a . l . Goldberger行走是一个随机漫步吗?远程相关性的证据在人类步态的步幅间隔,”<我>应用生理学杂志</我>,卷78,不。1,第358 - 349页,1995。<span class="reflinks">视图:<一个href="https://doi.org/10.1152/jappl.1995.78.1.349">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Is%20walking%20a%20random%20walk?%20Evidence%20for%20long-range%20correlations%20in%20stride%20interval%20of%20human%20gait&author=J. M. Hausdorff&author=C. K. Peng&author=Z. Ladin&author=J. Y. Wei&author=&author=A. L. Goldberger&publication_year=1995" target="_blank">谷歌学术搜索</一个></span></li> <li id="B3">l·莱莫恩k .老爹和d . Delignieres测试1 /的存在<我>f</我>继续挖掘数据中的噪音,”<我>加拿大《实验心理学/ Revue法裔加拿大女子de心理学Experimentale</我>,60卷,不。4、247 - 257年,2006页。<span class="reflinks">视图:<一个href="https://doi.org/10.1037/cjep2006023">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Testing%20for%20the%20presence%20of%201/f%20noise%20in%20continuation%20tapping%20data&author=L. Lemoine&author=K. Torre&author=&author=D. Delignières&publication_year=2006" target="_blank">谷歌学术搜索</一个></span></li> <li id="B4">C.-K。彭,j . Mietus j·m·豪斯多夫s Havlin h·e·斯坦利和a . l . Goldberger”远程anticorrelations和非高斯心跳的行为。”<我>物理评论快报</我>,卷70,不。9日,第1346 - 1343页,1993年。<span class="reflinks">视图:<一个href="https://doi.org/10.1103/physrevlett.70.1343">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Long-range%20anticorrelations%20and%20non-Gaussian%20behavior%20of%20the%20heartbeat&author=C.-K. Peng&author=J. Mietus&author=J. M. Hausdorff&author=S. Havlin&author=H. E. Stanley&author=&author=A. L. Goldberger&publication_year=1993" target="_blank">谷歌学术搜索</一个></span></li> <li id="B5">j·m·豪斯多夫”步态动力学在帕金森病:常见的步幅和不同的行为,步态变化,和碎片形缩放,”<我>混乱:一个跨学科的非线性科学》杂志上</我>,19卷,不。2、文章ID 026113, 2009。<span class="reflinks">视图:<一个href="https://doi.org/10.1063/1.3147408">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Gait%20dynamics%20in%20Parkinson’s%20disease:%20common%20and%20distinct%20behavior%20among%20stride%20length,%20gait%20variability,%20and%20fractal-like%20scaling&author=J. M. Hausdorff&publication_year=2009" target="_blank">谷歌学术搜索</一个></span></li> <li id="B6">n .亨特·d·麦格拉思,n . Stergiou”auditory-motor耦合在分形动力学的影响人类的步态,”<我>科学报告</我>,4卷,不。1,p。5879年,2014。<span class="reflinks">视图:<一个href="https://doi.org/10.1038/srep05879">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=The%20influence%20of%20auditory-motor%20coupling%20on%20fractal%20dynamics%20in%20human%20gait&author=N. Hunt&author=D. McGrath&author=&author=N. Stergiou&publication_year=2014" target="_blank">谷歌学术搜索</一个></span></li> <li id="B7">j . p . Kaipust d·麦格拉思·m·穆克吉和n . Stergiou”步态变化时改变老年人听听觉刺激不同时态的结构,“<我>《生物医学工程</我>第41卷。。8,1595 - 1603年,2013页。<span class="reflinks">视图:<一个href="https://doi.org/10.1007/s10439-012-0654-9">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Gait%20variability%20is%20altered%20in%20older%20adults%20when%20listening%20to%20auditory%20stimuli%20with%20differing%20temporal%20structures&author=J. P. Kaipust&author=D. McGrath&author=M. Mukherjee&author=&author=N. Stergiou&publication_year=2013" target="_blank">谷歌学术搜索</一个></span></li> <li id="B8">c . k .土卫五a·w·基弗s e D 'Andrea w·h·沃伦·r·k·亚伦,”夹带一个真正的时间分形视觉刺激调节分形步态动力学,”<我>人体运动科学</我>36卷,20 - 34,2014页。<span class="reflinks">视图:<一个href="https://doi.org/10.1016/j.humov.2014.04.006">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Entrainment%20to%20a%20real%20time%20fractal%20visual%20stimulus%20modulates%20fractal%20gait%20dynamics&author=C. K. Rhea&author=A. W. Kiefer&author=S. E. D’Andrea&author=W. H. Warren&author=&author=R. K. Aaron&publication_year=2014" target="_blank">谷歌学术搜索</一个></span></li> <li id="B9">d . Delignieres s Ramdani l·莱莫恩k .托瑞·m·福尔特斯人,g . Ninot”“短”时间序列的分形分析:重新古典方法,”<我>数学心理学杂志</我>,50卷,不。6,525 - 544年,2006页。<span class="reflinks">视图:<一个href="https://doi.org/10.1016/j.jmp.2006.07.004">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Fractal%20analyses%20for%20‘short’%20time%20series:%20a%20re-assessment%20of%20classical%20methods&author=D. Delignieres&author=S. Ramdani&author=L. Lemoine&author=K. Torre&author=M. Fortes&author=&author=G. Ninot&publication_year=2006" target="_blank">谷歌学术搜索</一个></span></li> <li id="B10">a .补充·赫尔曼·j·b·Bassingthwaighte et al .,“从运动生理时间序列:分形噪声的区别,”<我>弗鲁格档案:欧洲生理学杂志》上</我>,卷439,不。4、403 - 415年,2000页。<span class="reflinks">视图:<一个href="https://doi.org/10.1007/s004240050957">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Physiological%20time%20series:%20distinguishing%20fractal%20noises%20from%20motions&author=A. Eke&author=P. Herman&author=J. B. Bassingthwaighte et al.&publication_year=2000" target="_blank">谷歌学术搜索</一个></span></li> <li id="B11">a .补充·赫尔曼·l·柯奇士便因和l·r·科扎克”在颞生理信号的分形特性的复杂性<我>生理测量</我>,23卷,不。1,R1-R38, 2002页。<span class="reflinks">视图:<一个href="https://doi.org/10.1088/0967-3334/23/1/201">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Fractal%20characterization%20of%20complexity%20in%20temporal%20physiological%20signals&author=A. Eke&author=P. Herman&author=L. Kocsis&author=&author=L. R. Kozak&publication_year=2002" target="_blank">谷歌学术搜索</一个></span></li> <li id="B12">r . Jennane r . Harba, g . Jacquet”分数布朗运动的分析方法:理论和比较结果,“<我>特征信号</我>18卷,第436 - 419页,2001年。<span class="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Analysis%20methods%20for%20fractional%20Brownian%20motion:%20theory%20and%20comparative%20results&author=R. Jennane&author=R. Harba&author=&author=G. Jacquet&publication_year=2001" target="_blank">谷歌学术搜索</一个></span></li> <li id="B13">r·b·戴维斯和d·s·哈特,“赫斯特的测试效果,”<我>生物统计学</我>,卷74,不。1,第101 - 95页,1987。<span class="reflinks">视图:<一个href="https://doi.org/10.1093/biomet/74.1.95">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Tests%20for%20Hurst%20effect&author=R. B. Davies &author=D. S. Harte&publication_year=1987" target="_blank">谷歌学术搜索</一个></span></li> <li id="B14">s . Fatichi“ARFIMA模拟”,2009年,<一个t一个rget="_blank" href="https://www.mathworks.com/matlabcentral/fileexchange/25611-arfima-simulations">https://www.mathworks.com/matlabcentral/fileexchange/25611-arfima-simulations</一个>。<span class="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=ARFIMA%20simulations&author=S. Fatichi&publication_year=2009" target="_blank">谷歌学术搜索</一个></span></li> <li id="B15">d . Saupe“随机分形算法,”<我>分形图像的科学</我>、h·o·Peitgen和d . Saupe Eds。,pp。71–136, Springer, Berlin, Germany, 1988.<span class="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Algorithms%20for%20random%20fractals&author=D. Saupe&publication_year=1988" target="_blank">谷歌学术搜索</一个></span></li> <li id="B16">比比曼德布洛特和j·w·范·洛克,”分数布朗运动,部分噪音和应用程序”,<我>暹罗审查</我>,10卷,不。4、422 - 437年,1968页。<span class="reflinks">视图:<一个href="https://doi.org/10.1137/1010093">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Fractional%20Brownian%20motions,%20fractional%20noises%20and%20applications&author=B. B. Mandelbrot &author=J. W. Van Ness&publication_year=1968" target="_blank">谷歌学术搜索</一个></span></li> <li id="B17">1 / r·f·沃斯。<我>f</我>(闪烁)噪声:在简要回顾。<我>学报》第33届研讨会上频率控制</我>页40-46大西洋城,新泽西,美国,1979年5月- 6月。<span class="reflinks">视图:<一个href="https://doi.org/10.1109/FREQ.1979.200297">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=1/f%20(flicker)%20noise:%20a%20brief%20review&author=R. F. Voss" target="_blank">谷歌学术搜索</一个></span></li> <li id="B18">c·w·j·格兰杰和r . Joyeux介绍长记忆时间序列模型和分数差分,”<我>时间序列分析杂志》上</我>,1卷,不。1、15 - 29,1980页。<span class="reflinks">视图:<一个href="https://doi.org/10.1111/j.1467-9892.1980.tb00297.x">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=An%20introduction%20to%20long-memory%20time%20series%20models%20and%20fractional%20differencing&author=C. W. J. Granger &author=R. Joyeux&publication_year=1980" target="_blank">谷歌学术搜索</一个></span></li> <li id="B19">m . s . Taqqu诉Teverovsky, w .愿意“为远程依赖评估人员:一个实证研究,“<我>分形</我>,3卷,不。4、785 - 798年,1995页。<span class="reflinks">视图:<一个href="https://doi.org/10.1142/S0218348X95000692">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Estimators%20for%20long-range%20dependence:%20an%20empirical%20study&author=M. S. Taqqu&author=V. Teverovsky&author=&author=W. Willinger&publication_year=1995" target="_blank">谷歌学术搜索</一个></span></li> <li id="B20">p . Flandrin“分数布朗运动的光谱,”<我>IEEE信息理论</我>,35卷,不。1,第199 - 197页,1989。<span class="reflinks">视图:<一个href="https://doi.org/10.1109/18.42195">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=On%20the%20spectrum%20of%20fractional%20Brownian%20motions&author=P. Flandrin&publication_year=1989" target="_blank">谷歌学术搜索</一个></span></li> <li id="B21">d . Delignieres和诉Marmelat序列相关分析理论和方法论的问题,”<我>实验医学和生物学的发展</我>卷,782年,第148 - 127页,2013年。<span class="reflinks">视图:<一个href="https://doi.org/10.1007/978-1-4614-5465-6_7">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Theoretical%20and%20methodological%20issues%20in%20serial%20correlation%20analysis&author=D. Delignières &author=V. Marmelat&publication_year=2013" target="_blank">谷歌学术搜索</一个></span></li> <li id="B22">g . e . p .盒子,g·詹金斯g . c . Reinsel通用Ljung,<我>时间序列分析:预测与控制</我>美国旧金山,霍尔登天,CA, 1976。<span class="reflinks"></span></li> <li id="B23">m·福尔特斯人g . Ninot, d . Delignieres”对改编自回归综合移动平均过程:影响身体活动的研究,“<我>适应体育活动季度</我>,22卷,不。3、221 - 236年,2005页。<span class="reflinks">视图:<一个href="https://doi.org/10.1123/apaq.22.3.221">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=The%20auto-regressive%20integrated%20moving%20average%20procedures:%20implications%20for%20adapted%20physical%20activity%20research&author=M. Fortes&author=G. Ninot&author=&author=D. Delignières&publication_year=2005" target="_blank">谷歌学术搜索</一个></span></li> <li id="B24">j . Beran<我>长记忆过程的统计数据</我>美国佛罗里达州波卡拉顿,CRC新闻,1994年。<span class="reflinks"></span></li> <li id="B25">j . Beran y冯、美国Ghosh和r . Kulik<我>长记忆过程</我>施普林格,柏林,德国,2013年。<span class="reflinks">视图:<一个href="https://doi.org/10.1007/978-3-642-35512-7">出版商的网站</一个></span></li> <li id="B26">d . Delignieres k .老爹,l·莱莫恩”检测远程依赖通过ARFIMA模型和分形指数估计,“<我>英国心理学杂志上的数学和统计</我>,60卷,不。1,第106 - 85页,2007。<span class="reflinks">视图:<一个href="https://doi.org/10.1348/000711005X89513">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Detection%20of%20long-range%20dependence%20and%20estimation%20of%20fractal%20exponents%20through%20ARFIMA%20modelling&author=K. Torre&author=D. Delignières&author=&author=L. Lemoine&publication_year=2007" target="_blank">谷歌学术搜索</一个></span></li> <li id="B27">t . Stadnitski呈不规则碎片形研究的一些关键方面,“<我>非线性动力学、心理学、生命科学</我>》16卷,第158 - 137页,2012年。<span class="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Some%20critical%20aspects%20of%20fractality%20research&author=T. Stadnitski&publication_year=2012" target="_blank">谷歌学术搜索</一个></span></li> <li id="B28">d . Delignieres”相关的属性(离散)分数高斯噪声和分数布朗运动,”<我>数学问题在工程</我>ID 485623条,卷。2015年,7页,2015。<span class="reflinks">视图:<一个href="https://doi.org/10.1155/2015/485623">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Correlation%20properties%20of%20(discrete)%20fractional%20Gaussian%20noise%20and%20fractional%20Brownian%20motion&author=D. Delignières&publication_year=2015" target="_blank">谷歌学术搜索</一个></span></li> <li id="B29">z . m . h . Almurad和d . Delignieres均匀间隔的去趋势波动分析,“<我>自然史答:统计力学及其应用</我>卷,451年,第69 - 63页,2016年。<span class="reflinks">视图:<一个href="https://doi.org/10.1016/j.physa.2015.12.155">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Evenly%20spacing%20in%20detrended%20fluctuation%20analysis&author=Z. M. H. Almurad &author=D. Delignières&publication_year=2016" target="_blank">谷歌学术搜索</一个></span></li> <li id="B30">p . f .馥香,”红噪声频谱分析精度的过程使用最大熵和周期图方法:模拟研究和应用地球物理数据,”<我>地球物理研究杂志》</我>,卷90,不。A5, 4355 - 4366年,1985页。<span class="reflinks">视图:<一个href="https://doi.org/10.1029/JA090iA05p04355">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=On%20the%20accuracy%20of%20spectrum%20analysis%20of%20red%20noise%20processes%20using%20maximum%20entropy%20and%20periodogram%20methods:%20simulation%20studies%20and%20application%20to%20geophysical%20data&author=P. F. Fougere&publication_year=1985" target="_blank">谷歌学术搜索</一个></span></li> <li id="B31">g . Inzelt<我>最大似然估计的固定单变量ARFIMA (p d q)的过程</我>,2011,<一个t一个rget="_blank" href="https://fr.mathworks.com/matlabcentral/fileexchange/30238-arfima-p-d-q-estimator">https://fr.mathworks.com/matlabcentral/fileexchange/30238-arfima-p-d-q-estimator</一个>。<span class="reflinks"></span></li> <li id="B32">c . Diebolt诉Guiraud,“注意长记忆时间序列”<我>质量和数量</我>,39卷,不。6,827 - 836年,2005页。<span class="reflinks">视图:<一个href="https://doi.org/10.1007/s11135-004-0436-z">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=A%20note%20on%20long%20memory%20time%20series&author=C. Diebolt &author=V. Guiraud&publication_year=2005" target="_blank">谷歌学术搜索</一个></span></li> <li id="B33">d . c . Caccia d·珀西瓦尔·m·j .大炮g .雷蒙德和j·b·Bassingthwaighte”准确的分形时间序列分析:评估dispersional范围分析和新方法,”<我>自然史答:统计力学及其应用</我>,卷246,不。3 - 4、609 - 632年,1997页。<span class="reflinks">视图:<一个href="https://doi.org/10.1016/S0378-4371(97)00363-4">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Analyzing%20exact%20fractal%20time%20series:%20evaluating%20dispersional%20analysis%20and%20rescaled%20range%20methods&author=D. C. Caccia&author=D. Percival&author=M. J. Cannon&author=G. Raymond&author=&author=J. B. Bassingthwaighte&publication_year=1997" target="_blank">谷歌学术搜索</一个></span></li> <li id="B34">m . j .大炮d·b·珀西瓦尔d . c . Caccia g·m·雷蒙德和j·b·Bassingthwaighte”评估缩放窗口的方差估计的赫斯特系数时间序列方法,”<我>自然史答:统计力学及其应用</我>,卷241,不。3 - 4、606 - 626年,1997页。<span class="reflinks">视图:<一个href="https://doi.org/10.1016/S0378-4371(97)00252-5">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Evaluating%20scaled%20windowed%20variance%20methods%20for%20estimating%20the%20Hurst%20coefficient%20of%20time%20series&author=M. J. Cannon&author=D. B. Percival&author=D. C. Caccia&author=G. M. Raymond&author=&author=J. B. Bassingthwaighte&publication_year=1997" target="_blank">谷歌学术搜索</一个></span></li> <li id="B35">d . Delignieres k .老爹,p.l.。伯纳德,“从持久过渡到anti-persistent相关性姿势影响表明velocity的控制,”<我>PLoS计算生物学</我>,7卷,不。2篇文章ID e1001089 2011。<span class="reflinks">视图:<一个href="https://doi.org/10.1371/journal.pcbi.1001089">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Transition%20from%20persistent%20to%20anti-persistent%20correlations%20in%20postural%20sway%20indicates%20velocity-based%20control&author=D. Delignières&author=K. Torre&author=&author=P.-L. Bernard&publication_year=2011" target="_blank">谷歌学术搜索</一个></span></li> <li id="B36">d . g . Stephen j . Anastas,“分形波动凝视视觉搜索速度,”<我>注意、知觉和心理物理学</我>,卷73,不。3、666 - 677年,2011页。<span class="reflinks">视图:<一个href="https://doi.org/10.3758/s13414-010-0069-3">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Fractal%20fluctuations%20in%20gaze%20speed%20visual%20search&author=D. G. Stephen &author=J. Anastas&publication_year=2011" target="_blank">谷歌学术搜索</一个></span></li> <li id="B37">d . Delignieres l·莱莫恩,k .老爹,“时间间隔生产开发和振荡运动”,<我>人体运动科学</我>,23卷,不。2、87 - 103年,2004页。<span class="reflinks">视图:<一个href="https://doi.org/10.1016/j.humov.2004.07.001">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Time%20intervals%20production%20in%20tapping%20and%20oscillatory%20motion&author=D. Delignières&author=L. Lemoine&author=&author=K. Torre&publication_year=2004" target="_blank">谷歌学术搜索</一个></span></li> <li id="B38">E.-J。Wagenmakers, s·法雷尔和r·拉特克利夫称,”1 /评估和解释<我>fα</我>噪声在人类认知。”<我>心理计量学公告与评论</我>,11卷,不。4、579 - 615年,2004页。<span class="reflinks">视图:<一个href="https://doi.org/10.3758/BF03196615">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Estimation%20and%20interpretation%20of%201/fα%20noise%20in%20human%20cognition&author=E.-J. Wagenmakers&author=S. Farrell&author=&author=R. Ratcliff&publication_year=2004" target="_blank">谷歌学术搜索</一个></span></li> <li id="B39">g . Rangarajan周二和m .叮”综合方法在时间序列长程相关性的评估数据,”<我>物理评论E</我>,卷61,不。5,4991 - 5001年,2000页。<span class="reflinks">视图:<一个href="https://doi.org/10.1103/PhysRevE.61.4991">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Integrated%20approach%20to%20the%20assessment%20of%20long%20range%20correlation%20in%20time%20series%20data&author=G. Rangarajan &author=M. Ding&publication_year=2000" target="_blank">谷歌学术搜索</一个></span></li> <li id="B40">j . a . Doornik和m . Ooms<我>一个包裹估计、预测和模拟Arfima模型:Arfima包为1.0牛</我>荷兰鹿特丹伊拉斯姆斯大学,1999。<span class="reflinks"></span></li> <li id="B41">m . Ooms和j . a . Doornik”估计,模拟和预测分数自回归移动平均模型集成,”<我>第四届国际研讨会程序在计算经济和金融</我>英国剑桥,1998年。<span class="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Estimation,%20Simulation%20and%20Forecasting%20for%20Fractional%20Autoregressive%20Integrated%20Moving%20Average%20Models&author=M. Ooms &author=J. A. Doornik" target="_blank">谷歌学术搜索</一个></span></li> <li id="B42">j . a . Doornik<我>牛:面向对象语言矩阵</我>,贾斯汀顾问出版社,伦敦,英国,2001年。<span class="reflinks"></span></li> <li id="B43">k .刘和张x, y . Chen”评估ARFIMA(自回归部分积分移动平均)项目,“<我>公理</我>》第六卷,没有。4,p。2017。<span class="reflinks">视图:<一个href="https://doi.org/10.3390/axioms6020016">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=An%20evaluation%20of%20ARFIMA%20(autoregressive%20fractional%20integral%20moving%20average)%20programs&author=K. Liu&author=Y. Chen&author=&author=X. Zhang&publication_year=2017" target="_blank">谷歌学术搜索</一个></span></li> <li id="B44">E.-J。Wagenmakers, s·法雷尔和r·拉特克利夫称,“人类认知和一堆沙子:讨论串行和自组织临界性的相关性,”<我>实验心理学杂志》:一般</我>,卷134,不。1,第116 - 108页,2005。<span class="reflinks">视图:<一个href="https://doi.org/10.1037/0096-3445.134.1.108">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Human%20cognition%20and%20a%20pile%20of%20sand:%20a%20discussion%20on%20serial%20correlations%20and%20self-organized%20criticality&author=E.-J. Wagenmakers&author=S. Farrell&author=&author=R. Ratcliff&publication_year=2005" target="_blank">谷歌学术搜索</一个></span></li> <li id="B45">z . m . h . Almurad c . Roume h .痘痘和d . Delignieres”复杂性匹配:恢复运动的复杂性在老年人通过手挽着手散步,“<我>前沿生理学</我>,9卷,p。1766年,2018年。<span class="reflinks">视图:<一个href="https://doi.org/10.3389/fphys.2018.01766">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Complexity%20matching:%20restoring%20the%20complexity%20of%20locomotion%20in%20older%20people%20through%20arm-in-arm%20walking&author=Z. M. H. Almurad&author=C. Roume&author=H. Blain&author=&author=D. Delignieres&publication_year=2018" target="_blank">谷歌学术搜索</一个></span></li> <li id="B46">z . m . h . Almurad c Roume, d . Delignieres“复杂性匹配并排行走,”<我>人体运动科学</我>54卷,第136 - 125页,2017年。<span class="reflinks">视图:<一个href="https://doi.org/10.1016/j.humov.2017.04.008">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Complexity%20matching%20in%20side-by-side%20walking&author=Z. M. H. Almurad&author=C. Roume&author=&author=D. Delignières&publication_year=2017" target="_blank">谷歌学术搜索</一个></span></li> <li id="B47">j·m·豪斯多夫·米切尔,r . Firtion et al .,“改变分形动力学的步态:减少stride-interval相关性与衰老和亨廷顿氏舞蹈症,”<我>应用生理学杂志</我>,卷82,不。1,第269 - 262页,1997。<span class="reflinks">视图:<一个href="https://doi.org/10.1152/jappl.1997.82.1.262">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Altered%20fractal%20dynamics%20of%20gait:%20reduced%20stride-interval%20correlations%20with%20aging%20and%20Huntington’s%20disease&author=J. M. Hausdorff&author=S. L. Mitchell&author=R. Firtion et al.&publication_year=1997" target="_blank">谷歌学术搜索</一个></span></li> <li id="B48">n a“库兹涅佐夫”和c·k·瑞亚,“权力考虑去趋势波动分析的应用在步态变化的研究中,“<我>《公共科学图书馆•综合》</我>,12卷,不。第三条ID e0174144, 2017。<span class="reflinks">视图:<一个href="https://doi.org/10.1371/journal.pone.0174144">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Power%20considerations%20for%20the%20application%20of%20detrended%20fluctuation%20analysis%20in%20gait%20variability%20studies&author=N. A. Kuznetsov &author=C. K. Rhea&publication_year=2017" target="_blank">谷歌学术搜索</一个></span></li> <li id="B49">d . Delignieres诉Marmelat,“分形波动和复杂性:当前辩论和未来的挑战,”<我>生物医学工程的关键评论</我>,40卷,不。6,485 - 500年,2012页。<span class="reflinks">视图:<一个href="https://doi.org/10.1615/critrevbiomedeng.2013006727">出版商的网站</一个><span class="sep">|</span><a href="https://scholar.google.com/scholar_lookup?title=Fractal%20fluctuations%20and%20complexity:%20current%20debates%20and%20future%20challenges&author=D. Delignieres &author=V. Marmelat&publication_year=2012" target="_blank">谷歌学术搜索</一个></span></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</h4> <p>版权©2019克莱门特Roume et al。这是一个开放的分布式下文章<一个rel="license" href="http://creativecommons.org/licenses/by/4.0/">知识共享归属许可</一个>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</p> </div> </div> </article> </div> </div> </div> <div class="biblio__Wrapper-sc-1nou1lz-0 eyHfWh journal_article__BiblioIntegratorWidget-sc-12fk6zy-5 dbAANp article_widget biblioWrapper hide"> <hr> <h4 class="biblio__H4-sc-1nou1lz-2 becpDt hrTitleRef">更多相关文章</h4> <div id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 kCVTCa"></div> </div> </div> </div> <div class="threeColumn__RightWrapper-sc-1bf4078-2 jzTMLK rightWrapper" id="rightSectionMenu"> <div> <div class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-0 gbrQxi article_sticky_top_toolbar"> <div class="sc-cBdUnI hRnXob article_top_toolbar"> <a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-exkUMo hymroZ 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height="24"><span class="sc-dRFtgE jrsDZP">下载其他格式</span><span class="sc-gkFcWv gWTCXQ">更多的</span></span> <span class="sc-htoDjs bMdQcY sc-gbOuXE jGPvPL icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-fnwBNb etzuBr"> <a class="sc-htpNat bUhGXt link sc-iNhVCk gWgCNb open_panel" href="//www.newsama.com/downloads/journals/cmmm/2019/4025305.epub" aria-label="ePub" property="background-color" color="#D8D8D8"> <div class="sc-eAKXzc WHkfb"> ePub</d我v><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" 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height="24"><span class="sc-dRFtgE jrsDZP">订单打印副本</span><span class="sc-gkFcWv gWTCXQ">订单</span></span><span class="sc-htoDjs kNoiZu sc-gbOuXE jGPvPL right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-hBbWxd kdRRST"> <div class="sc-dyGzUR cHatnS"> <div> 的观点<span>918年</span> </div> <div> 下载<span>693年</span> </div> </div> <div> <div class="sc-drKuOJ kxdGAZ"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2019/4025305" data-style="small_circle"></span>引用</d我v> </div> </div> <nav class="sc-bRBYWo fXBKFa sc-hUfwpO jHPgUP" id="toolbar__iconNav"> <h3 class="sc-Rmtcm hNPrIr">分享文章</h3> <ul class="sc-hzDkRC bnbfTS"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2019/4025305&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" class="sc-EHOje jOLhQl socialTwitter" title="" role="presentation" 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