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<p>在这一页上</p> <span class="sc-fQejPQ fTFtno grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-fZwumE cLQMJq" href="#abstract" aria-label="">摘要</一个></span> <span class="sc-fQejPQ fTFtno grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-fZwumE cLQMJq" href="#introduction" aria-label="">介绍</一个></span> <span class="sc-fQejPQ fTFtno grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-fZwumE cLQMJq" href="#methods" aria-label="">方法</一个></span> <span class="sc-fQejPQ fTFtno grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-fZwumE cLQMJq" href="#results-and-discussion" aria-label="">结果与讨论</一个></span> <span class="sc-fQejPQ fTFtno grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-fZwumE cLQMJq" href="#conclusion-and-recommendations" aria-label="">结论</一个></span> <span class="sc-fQejPQ fTFtno grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-fZwumE cLQMJq" href="#data-availability" aria-label="">数据可用性</一个></span> <span class="sc-fQejPQ fTFtno grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-fZwumE cLQMJq" href="#conflicts-of-interest" aria-label="">的利益冲突</一个></span> <span class="sc-fQejPQ fTFtno grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-fZwumE cLQMJq" href="#references" aria-label="">参考文献</一个></span> <span class="sc-fQejPQ fTFtno grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-fZwumE cLQMJq" 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-cqCuEk dDomlX article_header_class"> <div class="sc-dliRfk HhtZN"> <span class="sc-kLIISr dybYoM">特殊的问题</span> <h2 class="sc-qrIAp kXQHAo">建模和正则回归中的应用</h2> <a class="sc-htpNat bUhGXt link sc-iqzUVk gFkWAn" href="//www.newsama.com/journals/jps/si/526168/" aria-label="">查看本特刊</一个> <hr class="sc-ebFjAB jhQWaL"> </div> <p class="sc-ipZHIp hDKZCZ article_type">研究论文|开放存取</p> <div class="sc-iGrrsa eZlme article_citation"> 体积 2020 <span class="sc-dEoRIm gusDuS">|</span>文章编号 1424020 <span class="sc-dEoRIm gusDuS">|</span> 10 页面 <span class="sc-dEoRIm gusDuS">|</span> <a class="sc-htpNat bUhGXt link sc-jtggT iUDBGe" href="https://doi.org/10.1155/2020/1424020" aria-label="Doi-link">https://doi.org/10.1155/2020/1424020</一个> </div> <h1 class="sc-jAaTju cxkaTM sc-bmyXtO gXrQDK article_title">利用高频数据预测阿拉比卡咖啡和原油价格的协波动性:一种多元GARCH方法</h1> </div> <div class="sc-jeCdPy bpzNtR article_authors"> <hr class="sc-likbZx PHYWq hr__author"> <span class=""><b>Dawit Yeshiwas</b><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail to Author Option"><img alt="" class="sc-EHOje cPuqxU sc-jtRlXQ jIaDFG" title="" role="presentation" 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src="data:image/svg+xml;base64,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" height="16"></a><sup>1</sup>和</span> <span class="">耶贝拉贝雷利<一个class="sc-htpNat bUhGXt link" href="https://orcid.org/0000-0001-7234-4804" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje cPuqxU sc-bGbJRg flqdYJ" title="" role="presentation" src="data:image/svg+xml;base64,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" height="16"></a><sup>1</sup></span> <div class="sc-ePZHVD eecoTM isHide"> <p><sup>1</sup><span>德布雷·马科斯大学科学学院统计系，德布雷·马科斯，埃塞俄比亚</span></p> </div> <button class="sc-kEYyzF gRIXYh sc-bEjcJn cFrLKZ" 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>拉希姆Alhamzawi</div> <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12月3日</span> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">修改后的</span> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2020年1月28日</span> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">公认</span> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2020年2月10</span> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发布时间</span> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2020年4月4日</span> </div> </div> </div> <article class="sc-kZmsYB kefHgx article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">摘要</h4> <p>预测资产收益率序列的covolatility正成为学者，从业者和投资组合经理之间进行了广泛研究的课题。本文估算各种使用阿拉伯咖啡的布伦特原油和周收盘价（单位：美元/磅）的周收盘价（美元/桶）多元GARCH模型，并比较了基于高频盘中这些模型的预测效果数据，其允许更精确的实现波动测量。这项研究使用的每周价格数据来明确模型covolatility和就业高频日内数据来评估模型预测效果。分析点的结论是，与学生的变化的条件相关性（VCC）模型<一世>Ť</一世>在我们的经验背景下，分布式创新术语是最精确的波动预测模型。我们建议并鼓励未来研究MGARCH模型预测性能的研究人员特别注意已实现波动的测量，在可行的情况下使用高频数据。</p> <span class="end-abs"></span> <h4 id="introduction">1.介绍</h4> <p>预测资产收益率序列的共变性正成为学术界、从业人员和投资组合经理广泛研究的课题[<一个href="#B1">1</一个>]。这已被用于风险管理、衍生品定价和对冲、投资组合选择和政策制定。同样，分析商品和资产价格之间的波动溢出效应，对于政府和投资者的风险管理和投资组合最大化具有深远的意义[<一个href="#B2">2</一个>]。鉴于目前国际市场的油价下跌，研究石油和咖啡价格之间的关系可以说是特别有意义的[<一个href="#B2">2</一个>]。最近，一些论文研究了石油价格与股票、农产品和贵金属价格的联动关系。</p> <p>先前的研究为石油和一个或多个市场之间的联系提供了证据。然而，这些研究大多集中在价格关联性上。相对而言，很少有研究致力于波动性的相关性。这令人惊讶，因为价格波动是期权和商品期货市场的主要驱动力。本文旨在弥补这一文献上的空白。特别地，它使用多元GARCH (MGARCH)族模型对两个重要的商品市场——石油和咖啡市场——之间的波动相关性进行了系统分析，以期提供一些严格的价格协波动预测模型。</p> <p>当然，在文献中不同的文件也倾向于学习的波动相互联系时，专注于不同的商品对。这项工作的重点是在商品期货市场，这是市场上其中一个可以在未来的一个特定时间以特定价格交付一套购买商品的具体量在布伦特原油和阿拉伯咖啡价格之间的covolatility。这些商品的选择的事实，这是世界上交易最活跃的商品的动机。现有的工作似乎主要集中在样本内大宗商品价格产生较小的注意模型预测效果的covolatility的造型。这项工作也将寻求弥合在文献中这种差距。</p> <p>最近的一些论文对能源和商品价格的共变系数进行了研究，主要是因为人们越来越关注了解这种共变系数在这些高度动荡时期的驱动因素和动态。文献中使用了替代估计方法，但到目前为止，还缺乏进行彻底的“MGARCH”分析的工作，这是一个特别适合于资产价格共变性建模的统计框架。此外，现有的研究大多集中在商品价格共变性的样本建模上，对模型预测性能的关注较少。因此，本文将试图通过对波动性预测绩效进行系统分析，为相关文献做出贡献。</p> <p>现有的波动溢出效应研究大多采用统计模型来估计实际波动率，而实际波动率往往是真实波动率的近似。基于模型的统计波动率的一个有吸引力的替代方法是基于高频日内数据或“tick”数据计算已实现的波动率。在预测潜在波动率方面，已实现波动率已被发现比基于模型的波动率更准确[<一个href="#B3">3</一个>]。因此，通过以往的研究提供的结果可能是潜在的，因为它们可能低估或高估了真实波动的程度产生误导。</p> <p>通过使用基于30分钟内数据的已实现的波动性，这项工作避免了这个潜在的陷阱。我们认为，这样做代表了一个重要的贡献，共同波动衡量的文献在商品市场。</p> <p>这项工作使文献以下贡献：<span class="list"><span class="list-item"><span class="list-label">（1）</span><span class="list-content">从应用计量经济学的角度，这项工作提供了一个稳健和系统的研究统计和计量性质的共波动率这两种重要的商品。</span></span><span class="list-item"><span class="list-label">（2）</span><span class="list-content">方向和在这个工作记录的咖啡和原油价格之间的相关性的大小，将有助于一个更明智决策的设计对金融机构以及其他利益相关者和市场参与者兴趣预见的波动的一部分这两个重要的商品。</span></span></span></p> <h4 id="methods">2.方法</h4> <h5 id="sec2.1">2.1。多元GARCH模型</h5> <p>大量文献涉及单变量模型价格序列。但是市场是相互作用的，因此从单变量模型到多变量模型的推广是很重要的。多元GARCH模型可分为四种类型[<一个href="#B4">4</一个>]。<span class="list"><span class="list-item"><span class="list-label">（一世）</span><span class="list-content">条件协方差矩阵模型：在这些模型中，直接计算条件协方差。向量误差校正（VEC）和Baba-Engle-Kraft-Kroner（BEKK）模型都属于这类模型。</span></span><span class="list-item"><span class="list-label">(2)</span><span class="list-content">因子模型：假设收益过程由少数不可观测的异方差因子组成。这种方法的优点在于，当与返回向量的维数相比，因子的数目较少时，问题的维数降低。</span></span><span class="list-item"><span class="list-label">（ⅲ）</span><span class="list-content">条件方差和相关模型：首先计算单变量条件方差和相关，然后利用它们得到条件协方差矩阵。一些模型是，例如，恒定条件相关（CCC）模型和动态条件相关（DCC）模型。</span></span><span class="list-item"><span class="list-label">(iv)</span><span class="list-content">非参数和半参数的方法：模型在这个类形成的条件协方差结构的参数估计的替代方案。这些模型的优势在于，他们不施加在数据上的特定分布（可错误指定）。</span></span></span></p> <p>本文采用条件方差模型和相关模型。在详细讨论MGARCH模型之前，先给出本系列的一些定义。本研究使用两种商品价格序列，得出双变量方法。<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="31.5646pt" id="M1-1" version="1.1" viewbox="0 0 65.824 31.5646" width="65.824pt" xmlns="http://www.w3.org/2000/svg" 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style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 10.6831 9.39034" width="10.6831pt" 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="#g113-234"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.89,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>是<svg height="8.98583pt" id="M7" style="vertical-align:-0.3499308pt" version="1.1" viewbox="-0.0498162 -8.6359 30.7815 8.98583" width="30.7815pt" 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="#g113-79"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.816,0)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.352,0)"> <use xlink:href="#g113-50"></use> </g> </svg>在时间预期收益的矢量<svg height="8.02022pt" id="M8" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -7.81382 4.54925 8.02022" 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</svg>;</span> <svg height="16.2017pt" id="M10" style="vertical-align:-3.943501pt" version="1.1" viewbox="-0.0498162 -12.2582 61.9154 16.2017" width="61.9154pt" 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="#g113-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.923,-5.741)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.355,-5.741)"> <use xlink:href="#g50-48"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,19.262,-5.741)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.075,3.784)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.412,0)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.227,0)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.764,0)"> <use xlink:href="#g113-79"></use> </g> </svg>是随时间变化的条件协方差矩阵的乔列斯基因子<span class="nowrap"> <svg height="13.3115pt" id="M11" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <path d="M697 -46L668 -39C637 -126 611 -142 545 -142H163L474 298L206 694H483C558 694 584 688 600 668C615 651 627 625 639 580L667 585L655 739H70V714L378 254L53 -203V-228H655L697 -46Z" id="g119-65"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>;</span>和<svg height="9.4347pt" id="M12" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.14359 9.93935 9.4347" width="9.93935pt" 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="#g113-123"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>是<svg height="8.98583pt" id="M13" style="vertical-align:-0.3499308pt" version="1.1" viewbox="-0.0498162 -8.6359 30.7815 8.98583" width="30.7815pt" 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="#g113-79"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.816,0)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.352,0)"> <use xlink:href="#g113-50"></use> </g> </svg>独立误差向量，均值为0，方差为1。</p> <p>条件不可预测分量的方差也可以定义为<span class="equation_break" id="EEq3"><span class="left_break" id="L14"></span><span class="middle_break"><span class="center_break" id="M14"> <svg height="33.8551pt" id="M14-1" version="1.1" viewbox="0 0 175.654 33.8551" width="175.654pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B14-1"> <g transform="matrix(.013,0,0,-0.013,0,19.214)"> <use xlink:href="#g121-116"></use> </g> <g transform="matrix(.013,0,0,-0.013,6.22,19.214)"> <use xlink:href="#g121-95"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.81,19.214)"> <use xlink:href="#g121-112"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.87,19.214)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.9,19.214)"> <use xlink:href="#g113-115"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,28.8,22.346)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.64,12.546)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.64,16.148)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.64,19.749)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.64,23.351)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.08,19.214)"> <use xlink:href="#g113-74"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.8,22.346)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,45.95,22.346)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.51,22.346)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.71,19.214)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.38,19.214)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.64,19.221)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,82.64,32.26)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,94.44,19.214)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,105.7,19.214)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,115.62,9.288)"> <path d="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 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transform="matrix(.0091,0,0,-0.0091,154.66,12.42)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,115.62,27.423)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,122.26,30.555)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,126.7,30.555)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,131.13,30.555)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,133.28,30.555)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,136.99,27.423)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,143.64,30.555)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,148.07,30.555)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,152.5,30.555)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,154.66,30.555)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,161.4,19.214)"> <use xlink:href="#g119-154"></use> </g> <g transform="matrix(.013,0,0,-0.013,172.69,19.214)"> <path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path> </g> </g> </svg> <svg class="alt_equation" height="33.8551pt" id="I14" version="1.1" viewbox="0 0 175.65 33.8551" width="175.65pt" 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="#B14-1"></use> </svg></span></span><span class="right_break" id="R14"> <svg class="label" height="11.44pt" id="M14-2" version="1.1" viewbox="0 0 14.868 11.44" width="14.868pt" 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,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.25)"> <path d="M269 381C298 400 325 421 340 436C360 455 370 476 370 504C370 579 313 635 223 635H222C170 635 123 610 95 579L52 516L72 497C95 533 136 577 193 577C245 577 286 546 286 482C286 408 218 369 127 339L133 314C149 319 174 325 197 325C254 325 324 285 324 192C325 83 266 39 201 39C143 39 103 68 78 91C70 98 62 97 54 91C45 84 33 71 32 58C30 46 34 35 48 22C61 10 102 -12 148 -12C216 -12 410 57 410 225C410 298 357 362 269 379V381Z" id="g190-232"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.37,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="33.8551pt" id="IL14" version="1.1" viewbox="0 0 14.92 33.8551" width="14.92pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 11)" xlink:href="#B14-2"></use> </svg></span></span></p> <p>在方程(<一个href="#EEq3">3</一个>)，得到的矩阵应该是对称的。此外，矩阵<svg height="13.3115pt" id="M15" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>所有的都是正的吗<span class="nowrap"> <svg height="8.02022pt" id="M16" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -7.81382 6.72451 8.02022" width="6.72451pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,2.175,0)"> <use xlink:href="#g113-117"></use> </g> </svg>。</span>多元建模方法带来了复杂性。首先，可能很难确保<svg height="13.3115pt" id="M17" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>是正定所有<span class="nowrap"> <svg height="8.02022pt" id="M18" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -7.81382 4.54925 8.02022" width="4.54925pt" 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="#g113-117"></use> </g> </svg>。</span>其次，参数的数量变得过大，难以估计，最后，可能难以获得系统的平稳性条件<span class="nowrap"> <svg height="13.3115pt" id="M19" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>。</span></p> <p>文献中提出的各种MGARCH模型在如何权衡其规范中的灵活性和节俭性方面存在差异<span class="nowrap"> <svg height="13.3115pt" id="M20" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>。</span>增加的灵活性允许模型捕获更复杂的<span class="nowrap"> <svg height="13.3115pt" id="M21" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>。</span>以下部分将描述的模型，其中所述血管内皮，DVEC模型它们是前人到CCC，VCC，和DCC模型首先描述的理论。</p> <h6 id="sec2.1.1">2.1.1。常数条件相关(CCC)模型</h6> <p>常数条件相关模型由Bollerslev [<一个href="#B5">五</一个>]，其中随时间变化的协方差矩阵<svg height="13.3115pt" id="M22" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>在时间<svg height="8.02022pt" id="M23" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -7.81382 4.54925 8.02022" width="4.54925pt" 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="#g113-117"></use> </g> </svg>表示为<span class="equation_break" id="EEq4"><span class="left_break" id="L24"></span><span class="middle_break"><span class="center_break" id="M24"> <svg height="26.8456pt" id="M24-1" version="1.1" viewbox="0 0 74.344 26.8456" width="74.344pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B24-1"> <g transform="matrix(.013,0,0,-0.013,0,12.211)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,4.99,25.251)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.79,12.205)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.23,12.205)"> <path d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z" id="g190-69"></path> </g> <g transform="matrix(.013,0,0,-0.013,39.85,12.205)"> <path d="M298 36L289 62C276 55 253 45 228 45C202 45 169 60 169 141V397H276C289 405 292 426 282 437H169V574L155 576L90 509V437H45L17 408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z" id="g190-117"></path> </g> <g transform="matrix(.013,0,0,-0.013,46.04,12.205)"> <path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" id="g113-83"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,54.13,15.336)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.8,12.205)"> <use xlink:href="#g190-69"></use> </g> <g transform="matrix(.013,0,0,-0.013,67.42,12.205)"> <use xlink:href="#g190-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,71.38,12.205)"> <path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g190-47"></path> </g> </g> </svg></span></span><span class="right_break" id="R24"> <svg class="label" height="11.44pt" id="M24-2" version="1.1" viewbox="0 0 15.458 11.44" width="15.458pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B24-2"> <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="M465 179V225H369V632H330C227 497 124 346 29 205V179H289V107C289 37 284 33 198 26V0H454V26C374 33 369 37 369 107V179H465ZM289 225H92C156 335 222 430 287 520H289V225Z" id="g190-166"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.96,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>右边是条件相关矩阵<svg height="8.8423pt" id="M25" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 8.28119 8.8423" width="8.28119pt" 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="#g113-83"></use> </g> </svg>这是时间不变的，即。，<svg height="11.927pt" id="M26" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 47.9589 11.927" width="47.9589pt" 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="#g113-83"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.386,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.648,0)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.8,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.764,0)"> <path d="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z" id="g113-69"></path> </g> </svg>是的对角矩阵（<span class="nowrap"> <svg height="13.639pt" id="M27" style="vertical-align:-4.35067pt" version="1.1" viewbox="-0.0498162 -9.28833 72.5881 13.639" width="72.5881pt" 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="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.643,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.075,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.233,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.924,0)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.567,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,27.998,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.683,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,36.826,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.969,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.112,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.288,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.432,0)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,64.075,3.132)"> <path d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 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xlink:href="#g119-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.45,107.469)"> <use xlink:href="#g119-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.45,115.038)"> <use xlink:href="#g119-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.45,122.606)"> <use xlink:href="#g119-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.45,144.697)"> <path d="M525 39V111H402C295 111 293 124 293 230V1733H212V39H525Z" id="g119-57"></path> </g> <g transform="matrix(.013,0,0,-0.013,48.55,15.029)"> <path d="M772 1098H727L517 -348H515L294 324L133 259L147 224L245 263L524 -588H526L772 1098Z" id="g119-122"></path> </g> <rect height="0.65243" width="16.9486" x="58.76" y=".702"></rect> <g transform="matrix(.013,0,0,-0.013,58.76,14.905)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,65.41,18.036)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.84,18.036)"> <use xlink:href="#g50-45"></use> </g> <g 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transform="matrix(.0091,0,0,-0.0091,69.84,65.539)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,72,65.539)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,60.64,80.493)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,60.64,85.723)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,60.64,90.953)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.43,114.829)"> <use xlink:href="#g119-122"></use> </g> <rect height="0.65243" width="27.1788" x="53.65" y="100.502"></rect> <g transform="matrix(.013,0,0,-0.013,53.65,114.704)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,60.29,117.836)"> <use xlink:href="#g50-108"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,64.92,117.836)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,70.48,117.836)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,74.92,117.836)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,77.07,117.836)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,48.45,138.58)"> <use xlink:href="#g119-122"></use> </g> <rect height="0.65243" width="17.1496" x="58.66" y="124.253"></rect> <g transform="matrix(.013,0,0,-0.013,58.66,138.456)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,65.31,141.587)"> <use xlink:href="#g50-108"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.94,141.587)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,72.1,141.587)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,24.218)"> <path d="M478 0V1724H165V1652H288C394 1652 397 1639 397 1488V0H478Z" id="g119-42"></path> </g> <g transform="matrix(.013,0,0,-0.013,86.81,31.787)"> <path d="M478 0V620H397V0H478Z" id="g119-50"></path> </g> <g transform="matrix(.013,0,0,-0.013,86.81,39.355)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,46.923)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,54.491)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,62.06)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,69.628)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,77.196)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,84.765)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,92.333)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,99.901)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,107.469)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,115.038)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,122.606)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.81,144.697)"> <path d="M478 39V1733H397V230C397 124 395 111 288 111H165V39H478Z" id="g119-58"></path> </g> <g transform="matrix(.013,0,0,-0.013,97.99,76.479)"> <use xlink:href="#g113-45"></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 14.898 11.44" width="14.898pt" 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,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M130 550H367L393 615L386 623H101L63 323C82 331 123 342 165 342C275 342 328 277 328 188C328 107 283 40 201 40C141 40 99 72 78 91C69 99 59 98 51 91C39 81 30 67 29 58C28 48 33 37 46 24C60 10 104 -12 149 -12C203 -11 269 14 323 59C384 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xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.348,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>遵循单变量GARCH过程。条件相关矩阵由<span class="nowrap"> <svg height="14.8173pt" id="M30" style="vertical-align:-5.52897pt" version="1.1" viewbox="-0.0498162 -9.28833 47.5414 14.8173" width="47.5414pt" 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="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.783,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.046,0)"> <path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z" id="g113-92"></path> </g> <g transform="matrix(.013,0,0,-0.013,27.531,0)"> <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 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162 -126 56 -136V-163H226Z" id="g113-94"></path> </g> </svg>，</span>和非对角元素<svg height="13.3115pt" id="M31" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>是<span class="equation_break" id="EEq6"><span class="left_break" id="L32"></span><span class="middle_break"><span class="center_break" id="M32"> <svg height="30.2617pt" id="M32-1" version="1.1" viewbox="0 0 86.374 30.2617" width="86.374pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B32-1"> <g transform="matrix(.013,0,0,-0.013,0,12.787)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,1,26.429)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,2.89,26.429)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.8,26.429)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.96,26.429)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.8,12.78)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.06,12.78)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,34.77,6.517)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,39.2,6.517)"> <use xlink:href="#g50-48"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,43.11,6.517)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,34.7,16.607)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,37.25,16.607)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,39.41,16.607)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,48.08,12.78)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,54.79,6.517)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.22,6.517)"> <use xlink:href="#g50-48"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,63.13,6.517)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,54.72,16.607)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.64,16.607)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,60.79,16.607)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,68.1,12.78)"> <use xlink:href="#g113-239"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,74.26,15.912)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,76.81,15.912)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,78.97,15.912)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,83.41,12.78)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="30.2617pt" id="M32-2" version="1.1" viewbox="0 0 34.384 30.2617" width="34.384pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B32-2"> <g transform="matrix(.013,0,0,-0.013,0,12.78)"> <path d="M563 650H502L416 416H157L71 650H10L256 -15H317L563 650ZM397 366L287 68H286L176 366H397Z" id="g117-46"></path> </g> <g transform="matrix(.013,0,0,-0.013,7.45,12.78)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.3,12.78)"> <path d="M-161 592L-215 609L-427 -83L-372 -100L-161 592Z" id="g117-145"></path> </g> <g transform="matrix(.013,0,0,-0.013,14.63,12.78)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.92,12.78)"> <path d="M394 607C394 634 378 655 350 655C315 655 294 620 294 594C294 564 314 546 339 546C372 546 394 574 394 607ZM360 349C373 414 374 448 351 448C321 448 249 404 183 338L197 313C223 336 265 367 276 367C285 367 283 355 275 313C241 129 220 23 189 -102C175 -158 153 -197 124 -197C106 -197 85 -187 70 -177C64 -173 51 -177 44 -183C34 -193 23 -209 23 -228C23 -244 46 -261 67 -261C86 -261 127 -245 181 -197C237 -147 279 -52 303 66L360 349Z" id="g113-107"></path> </g> <g transform="matrix(.013,0,0,-0.013,31.42,12.78)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R32"> <svg class="label" height="11.44pt" id="M32-3" 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="B32-3"> <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)"> <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></p> <p>期望的条件方差可以以矢量形式来表示：<span class="equation_break" id="EEq7"><span class="left_break" id="L33"></span><span class="middle_break"><span class="center_break" id="M33"> <svg height="39.5994pt" id="M33-1" version="1.1" viewbox="0 0 125.913 39.5994" width="125.913pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B33-1"> <g transform="matrix(.013,0,0,-0.013,0,22.124)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,5,35.164)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.8,22.118)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.06,22.118)"> <path d="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path> </g> <g transform="matrix(.013,0,0,-0.013,39.65,22.118)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,54.49,6.235)"> <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,-0.013,50.19,22.124)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,50.48,35.767)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,53.03,35.767)"> <path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,58.59,35.767)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.35,22.118)"> <path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,73.6,25.249)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,76.65,22.118)"> <use xlink:href="#g113-247"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,81.66,25.249)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,84.82,25.249)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,90.38,25.249)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,97.74,22.118)"> <path d="M573 255C573 407 448 530 294 530S15 407 15 255S140 -20 294 -20S573 103 573 255ZM521 255C521 127 419 24 294 24S67 127 67 255S169 486 294 486S521 383 521 255ZM350 255C350 288 326 313 294 313S238 288 238 255C238 220 262 197 294 197S350 220 350 255Z" id="g117-72"></path> </g> <g transform="matrix(.013,0,0,-0.013,108.28,22.118)"> <use xlink:href="#g113-247"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,113.61,15.854)"> <use xlink:href="#g50-31"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,113.28,25.902)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,116.44,25.902)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,122,25.902)"> <use xlink:href="#g50-107"></use> </g> </g> </svg> <svg height="39.5994pt" id="M33-2" version="1.1" viewbox="0 0 78.797 39.5994" width="78.797pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B33-2"> <g transform="matrix(.013,0,0,-0.013,0,22.118)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.79,6.235)"> <path d="M573 302C573 402 527 451 414 451C386 451 343 446 313 437L330 513L320 522C295 508 261 484 243 463L230 415C194 400 159 383 126 359L131 330C159 344 187 357 222 368L109 -147C96 -204 80 -214 18 -223L13 -255L256 -244L259 -212L236 -210C184 -205 180 -195 191 -141L219 -1C240 -10 268 -12 284 -12C352 4 431 48 484 104C543 166 573 240 573 302ZM481 290C481 165 381 37 305 37C280 37 249 56 235 71L302 395C328 399 353 402 372 402C427 402 481 378 481 290Z" id="g50-113"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.94,22.124)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.54,35.767)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.45,35.767)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.01,35.767)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.5,22.118)"> <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,-0.0091,32.25,25.249)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.85,22.124)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,39.09,35.767)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.25,35.767)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,47.81,35.767)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,54.2,22.118)"> <use xlink:href="#g117-72"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.78,7.353)"> <use xlink:href="#g50-31"></use> </g> <g transform="matrix(.013,0,0,-0.013,64.84,22.124)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,64.01,35.767)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,67.16,35.767)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,72.72,35.767)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,76.64,35.767)"> <path d="M117 -12C153 -12 178 12 178 50C178 84 153 110 118 110C84 110 59 84 59 50C59 12 84 -12 117 -12Z" id="g50-47"></path> </g> </g> </svg></span></span><span class="right_break" id="R33"> <svg class="label" height="11.44pt" id="M33-3" 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="B33-3"> <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)"> <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>第一项<一世>C</一世>是截距与的尺寸的载体<svg height="8.69875pt" id="M34" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 30.7346 8.69875" width="30.7346pt" 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="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path> </g> <g transform="matrix(.013,0,0,-0.013,11.607,0)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.319,0)"> <use xlink:href="#g113-50"></use> </g> </svg>和系数的矩阵是<span class="nowrap"> <svg height="7.35473pt" id="M35" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 16.485 7.35473" width="16.485pt" 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="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.806,0)"> <use xlink:href="#g113-111"></use> </g> </svg>。</span></p> <p>CCC模型的优点是，由于相关矩阵的存在，计算过程更容易进行<一世>[R</一世>是恒定的。然而，这意味着该模型可能过于严格[<一个href="#B6">6</一个>]。</p> <h6 id="sec2.1.2">2.1.2。动态条件相关(DCC)模型</h6> <p>动态条件相关模型如下<span class="equation_break" id="EEq8"><span class="left_break" id="L36"></span><span class="middle_break"><span class="center_break" id="M36"> <svg height="26.8456pt" id="M36-1" version="1.1" viewbox="0 0 79.704 26.8456" width="79.704pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B36-1"> <g transform="matrix(.013,0,0,-0.013,0,12.211)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,5,25.251)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.8,12.205)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.24,12.205)"> <use xlink:href="#g113-69"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.46,12.205)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.07,12.205)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,55.48,12.205)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,62.09,12.205)"> <use xlink:href="#g113-69"></use> </g> <g transform="matrix(.013,0,0,-0.013,72.31,12.205)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,76.74,12.205)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R36"> <svg class="label" height="11.44pt" id="M36-2" 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="B36-2"> <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>在哪里<svg height="13.3115pt" id="M37" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>是协方差矩阵和<svg height="8.8423pt" id="M38" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 15.167 8.8423" width="15.167pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,2.175,0)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.588,0)"> <use xlink:href="#g113-117"></use> </g> </svg>是<svg height="7.35473pt" id="M39" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 31.0217 7.35473" width="31.0217pt" 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="#g113-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.607,0)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.319,0)"> <use xlink:href="#g113-111"></use> </g> </svg>矩阵的条件相关的回报，这是对称的定义。的对角矩阵<svg height="8.8423pt" id="M40" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 14.8056 8.8423" width="14.8056pt" 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="#g113-69"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.219,0)"> <use xlink:href="#g113-117"></use> </g> </svg>表示为<span class="equation_break" id="EEq9"><span class="left_break" id="L41"></span><span class="middle_break"><span class="center_break" id="M41"> <svg height="14.9439pt" id="M41-1" version="1.1" viewbox="0 0 144.864 14.9439" width="144.864pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B41-1"> <g transform="matrix(.013,0,0,-0.013,0,10.593)"> <use xlink:href="#g113-69"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.89,13.725)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.19,10.593)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.46,10.593)"> <path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z" id="g190-101"></path> </g> <g transform="matrix(.013,0,0,-0.013,35.32,10.593)"> <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,-0.013,38.84,10.593)"> <path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z" id="g190-98"></path> </g> <g transform="matrix(.013,0,0,-0.013,44.49,10.593)"> <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(.013,0,0,-0.013,52.83,10.593)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.86,10.593)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,64.5,13.725)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,68.93,13.725)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,72.61,10.593)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.76,10.593)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,84.4,13.725)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,88.83,13.725)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,91.99,13.725)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,96.86,10.593)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,102,10.593)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,107.15,10.593)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,114.5,10.593)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,119.64,10.593)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,126.28,13.725)"> <use xlink:href="#g50-108"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,130.92,13.725)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,134.6,10.593)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,141.9,10.593)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R41"> <svg class="label" height="11.44pt" id="M41-2" 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="B41-2"> <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></span></span>其中每个<svg height="13.639pt" id="M42" style="vertical-align:-4.35067pt" version="1.1" viewbox="-0.0498162 -9.28833 15.1575 13.639" width="15.1575pt" 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="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.643,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.191,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.348,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>遵循单变量GARCH过程。此外，<svg height="13.3115pt" id="M43" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>必须是正定的，这是自动得到的<svg height="8.8423pt" id="M44" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 12.9918 8.8423" width="12.9918pt" 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="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.412,0)"> <use xlink:href="#g113-117"></use> </g> </svg>是相关矩阵是由定义对称的。当定义这个矩阵，需要两个要求。首先，<svg height="13.3115pt" id="M45" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>需要是正定的，因为它是协方差矩阵。第二，属于的部分<svg height="8.8423pt" id="M46" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 12.9918 8.8423" width="12.9918pt" 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="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.412,0)"> <use xlink:href="#g113-117"></use> </g> </svg>需要小于1。这些需求通过分解得到满足:<span class="equation_break" id="EEq10"><span class="left_break" id="L47"></span><span class="middle_break"><span class="center_break" id="M47"> <svg height="17.1152pt" id="M47-1" version="1.1" viewbox="0 0 11.238 17.1152" width="11.238pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B47-1"> <g transform="matrix(.013,0,0,-0.013,0,13.151)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.08,16.282)"> <use xlink:href="#g50-117"></use> </g> </g> </svg> <svg height="17.1152pt" id="M47-2" version="1.1" viewbox="0 0 71.052 17.1152" width="71.052pt" 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,-0.013,0,13.151)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.27,13.151)"> <use xlink:href="#g190-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.13,13.151)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.65,13.151)"> <use xlink:href="#g190-98"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.3,13.151)"> <use xlink:href="#g190-104"></use> </g> <g transform="matrix(.013,0,0,-0.013,35.64,13.151)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.67,13.151)"> <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(.0091,0,0,-0.0091,46.98,16.282)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,49.78,16.282)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,52.33,16.282)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.01,13.151)"> <use 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xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,54.05,16.282)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.73,13.151)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,62.78,5.85)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,68.34,5.85)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,75.49,13.151)"> <path d="M54 437L27 408L31 397H101V103C101 37 94 32 30 26V0H266V25C187 33 180 36 180 110V397H288C299 404 304 428 298 437H180V477C179 562 190 610 203 630C214 647 230 659 256 659C289 659 318 641 337 622C346 612 355 612 364 619C374 627 380 635 383 643C388 655 387 667 378 678C362 697 333 710 299 712C260 707 225 689 189 659C135 613 119 563 112 541S101 490 101 458V437H54Z" id="g190-103"></path> </g> <g transform="matrix(.013,0,0,-0.013,79.22,13.151)"> <path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 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transform="matrix(.013,0,0,-0.013,0,13.151)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.27,13.151)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.51,13.151)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.65,13.151)"> <path d="M717 427H488V399C559 390 569 378 549 331C530 287 513 253 489 216C425 282 354 343 321 371C360 397 383 416 402 432C423 450 444 479 444 520C444 600 377 658 296 658C208 658 132 590 132 500C132 446 159 403 204 361C119 300 54 260 54 167C54 80 125 -14 251 -14C323 -14 389 22 461 118C494 84 536 37 548 23C560 10 615 -13 670 -18L677 -9C647 49 556 150 514 191C549 244 573 285 601 324C634 373 647 391 717 399V427ZM285 624C335 624 369 576 369 519C369 465 342 426 295 391C235 437 204 472 204 524C204 584 239 624 285 624ZM278 54C212 54 139 100 139 196C139 245 164 292 230 339C321 265 385 204 438 145C405 99 345 54 278 54Z" id="g121-36"></path> </g> <g transform="matrix(.013,0,0,-0.013,31.97,13.151)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.12,13.151)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.64,13.151)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="43.0972pt" id="I47" version="1.1" viewbox="0 0 172.4 43.0972" width="172.4pt" 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="#B47-1"></use> <use transform="matrix(1 0 0 1 15.38 0)" xlink:href="#B47-2"></use> <use transform="matrix(1 0 0 1 10.69 25.982)" xlink:href="#B47-3"></use> <use transform="matrix(1 0 0 1 16.56 25.98)" xlink:href="#B47-4"></use> <use transform="matrix(1 0 0 1 123.4 25.98)" xlink:href="#B47-5"></use> </svg></span></span><span class="right_break" id="R47"> <svg class="label" height="11.44pt" id="M47-6" 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="B47-6"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.25)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.82,9.25)"> <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,-0.013,15.23,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="43.0972pt" id="IL47" version="1.1" viewbox="0 0 19.81 43.0972" 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 15.62)" xlink:href="#B47-6"></use> </svg></span></span>在哪里<span class="equation_break" id="EEq11"><span class="left_break" id="L48"></span><span class="middle_break"><span class="center_break" id="M48"> <svg height="18.3157pt" id="M48-1" version="1.1" viewbox="0 0 170.002 18.3157" width="170.002pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B48-1"> <g transform="matrix(.013,0,0,-0.013,0,12.485)"> <use xlink:href="#g113-82"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.32,15.617)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.62,12.485)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.89,12.485)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.91,12.485)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.05,12.485)"> <path d="M535 230V280H52V230H535Z" id="g117-33"></path> </g> <g transform="matrix(.013,0,0,-0.013,52.59,12.485)"> <path d="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 379 25 341L43 318C81 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transform="matrix(.0091,0,0,-0.0091,165.57,16.269)"> <use xlink:href="#g50-50"></use> </g> </g> </svg> <svg height="18.3157pt" id="M48-2" version="1.1" viewbox="0 0 57.406 18.3157" width="57.406pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B48-2"> <g transform="matrix(.013,0,0,-0.013,0,12.485)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.53,12.485)"> <use xlink:href="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.89,15.617)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.84,12.485)"> <use xlink:href="#g113-82"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,32.16,15.617)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,35.32,15.617)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,40.88,15.617)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,45.31,15.617)"> <use xlink:href="#g50-45"></use> </g> <rect height="0.65243" width="9.4212" x="48.02" y="1.289"></rect> <g transform="matrix(.013,0,0,-0.013,48.02,12.485)"> <use xlink:href="#g113-82"></use> </g> </g> </svg> <svg height="18.3157pt" id="M48-3" version="1.1" viewbox="0 0 60.153 18.3157" width="60.153pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B48-3"> <g transform="matrix(.013,0,0,-0.013,0,12.485)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.27,12.485)"> <path d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z" id="g121-97"></path> </g> <g transform="matrix(.013,0,0,-0.013,16.77,12.485)"> <path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 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transform="matrix(.0091,0,0,-0.0091,40.5,16.269)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,44.62,12.485)"> <use xlink:href="#g119-130"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.2,12.485)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="70.3761pt" id="I48" version="1.1" viewbox="0 0 172.88 70.3761" width="172.88pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -0.53)" xlink:href="#B48-1"></use> <use transform="matrix(1 0 0 1 30.85 24.88)" xlink:href="#B48-2"></use> <use transform="matrix(1 0 0 1 91.93 24.88)" xlink:href="#B48-3"></use> <use transform="matrix(1 0 0 1 16.65 52.06)" xlink:href="#B48-4"></use> </svg></span></span><span class="right_break" id="R48"> <svg class="label" height="11.44pt" id="M48-5" 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="B48-5"> <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="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.9,9.25)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.29,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="70.3761pt" id="IL48" version="1.1" viewbox="0 0 17.86 70.3761" width="17.86pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 29.26)" xlink:href="#B48-5"></use> </svg></span></span>在哪里<svg height="14.0487pt" id="M49" style="vertical-align:-2.1506pt" version="1.1" viewbox="-0.0498162 -11.8981 9.52083 14.0487" width="9.52083pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <rect height="0.65243" width="9.4212" x="0" y="-11.1958"></rect> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-82"></use> </g> </svg>当模型包含有限的参数和向量时，无条件协方差是否有限<svg height="9.25202pt" id="M50" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 8.79107 9.25202" width="8.79107pt" 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="#g113-247"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,5.005,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>具有有限方差。此外,参数<svg height="9.14241pt" id="M51" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 12.4317 9.14241" width="12.4317pt" 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="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.358,3.132)"> <use xlink:href="#g50-50"></use> </g> </svg>和<svg height="9.14241pt" id="M52" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 12.4317 9.14241" width="12.4317pt" 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="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.358,3.132)"> <use xlink:href="#g50-51"></use> </g> </svg>标量和<svg height="12.7112pt" id="M53" style="vertical-align:-3.403299pt" version="1.1" viewbox="-0.0498162 -9.3079 42.9217 12.7112" width="42.9217pt" 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="#g190-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,6.864,0)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.387,0)"> <use xlink:href="#g190-98"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.029,0)"> <use xlink:href="#g190-104"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.371,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> </g> <g transform="matrix(.013,0,0,-0.013,28.869,0)"> <use xlink:href="#g113-82"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.255,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> </g> </svg>是用来缩放的<svg height="10.7866pt" id="M54" style="vertical-align:-2.150701pt" version="1.1" viewbox="-0.0498162 -8.6359 14.2314 10.7866" width="14.2314pt" 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="#g113-82"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.647,0)"> <use xlink:href="#g113-117"></use> </g> </svg>为了实现这个目标<span class="inline_break"> <svg height="15.6042pt" id="M55" style="vertical-align:-6.31587pt" version="1.1" viewbox="-0.0498162 -9.28833 58.79 15.6042" width="58.79pt" 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="M162 -163V703H101V-163H162Z" id="g113-9"></path> </g> <g transform="matrix(.013,0,0,-0.013,3.419,0)"> <use xlink:href="#g113-239"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.581,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.462,3.132)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.898,0)"> <use xlink:href="#g113-9"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.948,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.211,0)"> <use xlink:href="#g113-9"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.63,0)"> <use xlink:href="#g113-114"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,43.948,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,45.83,3.132)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,49.743,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.434,0)"> <path d="M368 703H309L44 -163H104L368 703Z" id="g113-48"></path> </g> </svg><span class="isep"></span> <svg height="15.6042pt" style="vertical-align:-6.31587pt" version="1.1" viewbox="58.7451838 -9.28833 46.602 15.6042" width="46.602pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,58.795,2.377)"> <path d="M778 808H735L485 -141H483L284 324L133 247L149 215L244 263L484 -298H486L778 808Z" id="g119-121"></path> </g> <rect height="0.65243" width="32.9068" x="68.8299" y="-8.16591"></rect> <g transform="matrix(.013,0,0,-0.013,68.83,0)"> <use xlink:href="#g113-114"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,75.148,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,77.943,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,80.491,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,84.177,0)"> <use xlink:href="#g113-114"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,90.495,3.132)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,94.08,3.132)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,97.994,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,101.737,0)"> <use xlink:href="#g113-9"></use> </g> </svg></span>≤1,<svg height="11.4899pt" id="M56" style="vertical-align:-5.52899pt" version="1.1" viewbox="-0.0498162 -5.96091 12.7578 11.4899" width="12.7578pt" 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="#g113-114"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.318,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.199,3.132)"> <use xlink:href="#g50-107"></use> </g> </svg>是矩阵的元素<span class="nowrap"> <svg height="12.7112pt" id="M57" style="vertical-align:-3.403299pt" version="1.1" viewbox="-0.0498162 -9.3079 42.9217 12.7112" width="42.9217pt" 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="#g190-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,6.864,0)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.387,0)"> <use xlink:href="#g190-98"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.029,0)"> <use xlink:href="#g190-104"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.371,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.869,0)"> <use xlink:href="#g113-82"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.255,0)"> <use xlink:href="#g113-42"></use> </g> </svg>。</span>估计<svg height="14.0487pt" id="M58" style="vertical-align:-2.1506pt" version="1.1" viewbox="-0.0498162 -11.8981 9.52083 14.0487" width="9.52083pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <rect height="0.65243" width="9.4212" x="0" y="-11.1958"></rect> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-82"></use> </g> </svg>是<span class="equation_break" id="EEq12"><span class="left_break" id="L59"></span><span class="middle_break"><span class="center_break" id="M59"> <svg height="37.4399pt" id="M59-1" version="1.1" viewbox="0 0 68.984 37.4399" width="68.984pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B59-1"> <g transform="matrix(.013,0,0,-0.013,1.01,19.482)"> <path d="M658 557C549 593 437 629 340 673H318C222 629 109 593 0 557L9 532C116 551 225 577 329 602C435 576 543 551 649 532L658 557Z" id="g119-105"></path> </g> <g transform="matrix(.013,0,0,-0.013,0,22.379)"> <use xlink:href="#g113-82"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.06,22.379)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.54,13.871)"> <use xlink:href="#g113-50"></use> </g> <rect height="0.65243" width="8.31205" x="25.51" y="18.725"></rect> <g transform="matrix(.013,0,0,-0.013,25.51,31.604)"> <path d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z" id="g113-85"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,38.68,7.614)"> <path d="M655 676H628C608 656 600 650 571 650H156C118 650 114 651 102 676H77C63 615 45 548 24 485L60 486C81 531 97 562 114 580C134 603 148 611 252 611H308L217 127C201 41 196 38 105 32L98 0H384L393 32C300 38 288 41 304 127L393 611H466C553 611 571 604 582 580C592 559 597 530 595 485L630 489C636 548 645 624 655 676Z" id="g50-85"></path> </g> <g transform="matrix(.013,0,0,-0.013,35.04,22.385)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,35.02,35.845)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.18,35.845)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,43.74,35.845)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,48.22,22.379)"> <use xlink:href="#g113-247"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,53.23,25.51)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.89,22.379)"> <use xlink:href="#g113-247"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,62.22,16.115)"> <use xlink:href="#g50-31"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,61.9,26.163)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.02,22.379)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R59"> <svg class="label" height="11.44pt" id="M59-2" 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="B59-2"> <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></span></span></p> <p>此外，标量<svg height="9.14241pt" id="M60" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 12.4317 9.14241" width="12.4317pt" 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="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.358,3.132)"> <use xlink:href="#g50-50"></use> </g> </svg>和<svg height="9.14241pt" id="M61" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 12.4317 9.14241" width="12.4317pt" 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="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.358,3.132)"> <use xlink:href="#g50-51"></use> </g> </svg>必须大于零，但总和必须小于一。人们可能会注意到，这些是单变量GARCH保持平稳的条件，但在DCC模型中也适用[<一个href="#B7">7</一个>]。</p> <h6 id="sec2.1.3">2.1.3。变化的条件相关（VCC）模型</h6> <p>变条件相关(VCC)是一种多元广义自回归条件异方差(MGARCH)模型，其中条件方差被建模为单变量GARCH模型，条件协方差被建模为条件方差的非线性函数。加权条件方差的非线性组合的条件相关参数遵循Tse和Tsui指定的GARCH-like过程[<一个href="#B6">6</一个>]。VCC MGARCH模型与密切相关的动态条件相关MGARCH模型一样灵活，比常数条件相关模型更灵活，比对角向量条件偏差(DVECH)模型更简洁。</p> <p>对于扰动的时变条件协方差矩阵，MGARCH模型在其规范的简约性和灵活性上有所不同，用表示<span class="nowrap"> <svg height="13.3115pt" id="M62" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>。</span>在多元GARCH模型，对角线元素的条件相关族<svg height="13.3115pt" id="M63" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>被建模为单变量GARCH模型，而非对角元素被建模作为对角线项的非线性函数。在VCC多元GARCH模型，<span class="equation_break" id="EEq13"><span class="left_break" id="L64"></span><span class="middle_break"><span class="center_break" id="M64"> <svg height="22.7523pt" id="M64-1" version="1.1" viewbox="0 0 102.074 22.7523" width="102.074pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B64-1"> <g transform="matrix(.013,0,0,-0.013,0,14.946)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.65,18.077)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.53,18.077)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.44,18.077)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.6,18.077)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.93,14.946)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.19,14.946)"> <use xlink:href="#g113-239"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,39.35,18.077)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,41.23,18.077)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,45.15,18.077)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,47.3,18.077)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,51,15.03)"> <use xlink:href="#g119-122"></use> </g> <rect height="0.65243" width="37.8888" x="61.22" y=".702"></rect> <g transform="matrix(.013,0,0,-0.013,61.22,14.946)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,67.86,18.077)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,70.66,18.077)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,73.21,18.077)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,75.36,18.077)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,79.06,14.946)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,85.7,18.077)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,89.29,18.077)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,93.2,18.077)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,95.36,18.077)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,99.11,14.946)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R64"> <svg class="label" height="11.44pt" id="M64-2" 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="B64-2"> <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>其中对角元素<svg height="10.8649pt" id="M65" style="vertical-align:-1.57657pt" version="1.1" viewbox="-0.0498162 -9.28833 24.3441 10.8649" width="24.3441pt" 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="#g113-105"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.1,0)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.04,0)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.59,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,19.733,0)"> <use xlink:href="#g113-117"></use> </g> </svg>和<svg height="12.7178pt" id="M66" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 25.91 12.7178" width="25.91pt" 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="#g113-105"></use> </g> <g transform="matrix(.013,0,0,-0.013,5.664,0)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.643,0)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.143,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.286,0)"> <use xlink:href="#g113-117"></use> </g> </svg>遵循单变量GARCH流程<svg height="12.0653pt" id="M67" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -8.6359 25.1662 12.0653" width="25.1662pt" 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(.013,0,0,-0.013,7.402,0)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.907,0)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.407,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.55,0)"> <use xlink:href="#g113-117"></use> </g> </svg>遵循谢霆锋及徐锦江[<一个href="#B6">6</一个>]和下面所讨论的。因为<svg height="12.0653pt" id="M68" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -8.6359 25.1662 12.0653" width="25.1662pt" 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(.013,0,0,-0.013,7.402,0)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.907,0)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.407,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.55,0)"> <use xlink:href="#g113-117"></use> </g> </svg>随着时间的变化，这个模型被称为VCC GARCH模型。</p> <p>在VCC-GARCH（1，1）模型提出谢和咀[<一个href="#B6">6</一个>]可以写为<span class="equation_break" id="EEq14"><span class="left_break" id="L69"></span><span class="middle_break"><span 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transform="matrix(.0091,0,0,-0.0091,43.01,28.636)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,33.82,38.684)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.98,34.9)"> <use xlink:href="#g113-123"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,54.13,38.031)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.8,34.9)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="98.0009pt" id="M69-3" version="1.1" viewbox="0 0 69.904 98.0009" width="69.904pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B69-3"> <g transform="matrix(.013,0,0,-0.013,0,59.942)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,5,72.982)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.8,59.936)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.06,59.936)"> <use xlink:href="#g113-69"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,37.95,63.067)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.62,59.936)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,49.71,63.067)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.38,59.936)"> <use xlink:href="#g113-69"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,63.27,63.067)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.94,59.936)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="98.0009pt" id="M69-4" version="1.1" viewbox="0 0 148.982 98.0009" width="148.982pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B69-4"> <g transform="matrix(.013,0,0,-0.013,0,94.036)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.09,97.168)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.39,94.036)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.65,94.036)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.67,94.036)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.82,94.036)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.36,94.036)"> <use xlink:href="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.71,97.168)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.57,94.036)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.1,94.036)"> <use xlink:href="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,84.46,97.168)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,89.41,94.036)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,96.75,94.036)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,107.8,94.036)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,118.34,94.036)"> <use xlink:href="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,125.7,97.168)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,130.64,94.036)"> <use xlink:href="#g113-227"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,135.83,97.168)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,138.99,97.168)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,144.55,97.168)"> <use xlink:href="#g50-50"></use> </g> </g> </svg> <svg height="98.0009pt" id="M69-5" version="1.1" viewbox="0 0 47.594 98.0009" width="47.594pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B69-5"> <g transform="matrix(.013,0,0,-0.013,0,94.036)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.54,94.036)"> <use xlink:href="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.9,97.168)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.84,94.036)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,30.93,97.168)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,34.09,97.168)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,39.65,97.168)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,44.63,94.036)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="119.02pt" id="I69" version="1.1" viewbox="0 0 151.07 119.02" width="151.07pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 4.58 0)" xlink:href="#B69-1"></use> <use transform="matrix(1 0 0 1 4.29 0)" xlink:href="#B69-2"></use> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B69-3"></use> <use transform="matrix(1 0 0 1 1.38 0)" xlink:href="#B69-4"></use> <use transform="matrix(1 0 0 1 30.99 21.02)" xlink:href="#B69-5"></use> </svg></span></span><span class="right_break" id="R69"> <svg class="label" height="11.44pt" id="M69-6" 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="B69-6"> <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="119.02pt" id="IL69" version="1.1" viewbox="0 0 19.72 119.02" width="19.72pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 53.58)" xlink:href="#B69-6"></use> </svg></span></span>在哪里<svg height="9.25202pt" id="M70" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 10.9963 9.25202" width="10.9963pt" 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="#g50-117"></use> </g> </svg>是一个<svg height="9.63826pt" id="M71" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -9.28833 26.3971 9.63826" width="26.3971pt" 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="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z" id="g113-108"></path> </g> <g transform="matrix(.013,0,0,-0.013,9.445,0)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,19.981,0)"> <use xlink:href="#g113-50"></use> </g> </svg>向量的自变量，其中可能包含的滞后<span class="nowrap"> <svg height="9.25202pt" id="M72" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 8.68666 9.25202" width="8.68666pt" 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="#g113-115"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>;</span> <svg height="9.49473pt" id="M73" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.59789 9.49473" width="6.59789pt" 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="#g113-230"></use> </g> </svg>是一个<svg height="9.63826pt" id="M74" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -9.28833 30.4292 9.63826" width="30.4292pt" 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="M766 88L752 113C719 83 690 64 681 64C674 64 672 74 679 103L724 292C758 436 724 448 701 448C680 448 666 442 639 429C594 407 514 350 441 252H439L447 289C476 423 450 448 419 448C398 448 379 441 355 427C307 400 234 344 162 249H160L180 324C203 409 197 448 170 448C144 448 82 413 23 349L35 321C57 343 96 374 108 374C115 374 117 371 111 341C87 227 57 112 24 -6L32 -12C53 -4 81 4 108 6C119 68 134 128 149 171C177 229 309 383 364 383C387 383 388 355 373 282C354 190 330 92 303 -6L309 -12C332 -4 356 3 386 6C396 63 411 122 424 171C458 236 590 383 642 383C658 383 664 369 652 315L603 91C587 20 593 -12 619 -12C642 -12 708 23 766 88Z" id="g113-110"></path> </g> <g transform="matrix(.013,0,0,-0.013,13.163,0)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.699,0)"> <use xlink:href="#g113-108"></use> </g> </svg>矩阵的参数;<svg height="9.25202pt" id="M75" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 8.68666 9.25202" width="8.68666pt" 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="#g113-115"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>是一个<svg height="8.69875pt" id="M76" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 30.1291 8.69875" width="30.1291pt" 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="#g113-110"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.163,0)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.699,0)"> <use xlink:href="#g113-50"></use> </g> </svg>因变量向量;<svg height="16.2017pt" id="M77" style="vertical-align:-3.943501pt" version="1.1" viewbox="-0.0498162 -12.2582 24.3738 16.2017" width="24.3738pt" 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="#g113-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.923,-5.741)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.355,-5.741)"> <use xlink:href="#g50-48"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,19.262,-5.741)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.075,3.784)"> <use xlink:href="#g50-117"></use> </g> </svg>是随时间变化的条件协方差矩阵的乔列斯基因子<span class="nowrap"> <svg height="13.3115pt" id="M78" style="vertical-align:-3.625179pt" version="1.1" viewbox="-0.0498162 -9.68632 13.5539 13.3115" width="13.5539pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,.007)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.787,3.466)"> <use xlink:href="#g50-117"></use> </g> </svg>;</span> <svg height="9.4347pt" id="M79" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.14359 9.93935 9.4347" width="9.93935pt" 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="#g113-123"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>是一个<svg height="8.69875pt" id="M80" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 30.1291 8.69875" width="30.1291pt" 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="#g113-110"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.163,0)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.699,0)"> <use xlink:href="#g113-50"></use> </g> </svg>独立和同分布创新向量;和<svg height="11.927pt" id="M81" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 13.6974 11.927" width="13.6974pt" 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="#g113-69"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.893,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>是一个条件标准差的对角矩阵。<span class="inline_break"> <svg height="12.7112pt" id="M82" style="vertical-align:-3.403299pt" version="1.1" viewbox="-0.0498162 -9.3079 72.872 12.7112" width="72.872pt" 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="#g113-69"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.893,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.192,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.455,0)"> <use xlink:href="#g190-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,35.319,0)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.842,0)"> <use xlink:href="#g190-98"></use> </g> <g transform="matrix(.013,0,0,-0.013,44.484,0)"> <use xlink:href="#g190-104"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.651,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,55.149,0)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,61.792,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,66.224,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,69.908,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="12.7112pt" style="vertical-align:-3.403299pt" version="1.1" viewbox="75.0011838 -9.3079 17.723 12.7112" width="17.723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,75.051,0)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,81.694,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,86.126,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,89.81,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="12.7112pt" style="vertical-align:-3.403299pt" version="1.1" viewbox="94.9041838 -9.3079 18.426 12.7112" width="18.426pt" xmlns="http://www.w3.org/2000/svg" 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[<一个href="#B8">8</一个>]，示出了返回不是正态分布。相反，学生<一世>Ť</一世>分布以比正态分布更充分的方式捕捉经验回报中观察到的峰度。与正态分布相比，收益具有更多的峰度和更肥的尾部。因此,学生<一世>Ť</一世>分布更适合[<一个href="#B9">9</一个>]。当使用GARCH模型时，通常使用三个关于误差项的条件分布的假设:正态(高斯)分布，学生的<一世>Ť</一世>以及广义误差分布(GED)。</p> <h5 id="sec2.3">2.3。推断评价</h5> <p>评价是有多种方法来完成。MAE，RMSE，并从一个普通最小二乘回归解释能力：首先，估计使用三种措施的方法相比。其次，试图确定残差的拟合优度通过由与Ljung的芯盒测试分析的单变量的方法来完成。</p> <h6 id="sec2.3.1">2.3.1。定义一个代理</h6> <p>在评估波动的预测，对“真”的波动通常的代理是“事后”平方收益或误差平方。然而，正如安德森和Bollerslev [注意<一个href="#B5">五</一个>，尽管作为对波动过程的无偏估计，平方回报或平方误差的使用是合理的，但由于它是一个很大的特殊术语，它提供了一个非常嘈杂的度量。具体来说，回报创新可以写成<svg height="9.4347pt" id="M89" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.14359 44.0071 9.4347" width="44.0071pt" 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="#g113-247"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,5.005,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.304,0)"> <use 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transform="matrix(.013,0,0,-0.013,124.243,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,132.373,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,143.636,0)"> <use xlink:href="#g113-240"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,150.983,-5.741)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,150.396,3.784)"> <use xlink:href="#g50-117"></use> </g> </svg>，和的平方误差是波动过程的无偏估计;然而，它仍包含嘈杂的特质来看，<span class="nowrap"> <svg height="15.535pt" id="M95" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 11.5443 15.535" width="11.5443pt" 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="#g113-123"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.475,-5.741)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.149,3.784)"> <use xlink:href="#g50-117"></use> </g> </svg>。</span>这通常导致了表现不佳，其中策动波动模型的实际意义的讨论。</p> <p>Hansen等人。[<一个href="#B10">10</一个>提供的另一个重要的参数使用实现差异而不是方的回报。他们指出，替代的条件方差可能会严重扭曲的比较，在这个意义上的平方回报的经验排名的模型可以用于真正的（人口）不一致的排名。所以，这是基于平方回报率的评估可能的概率选择劣质模型作为“最佳”收敛于一个样本容量的增加。出于这个原因，我们的评估是基于实现差异。在这条线的研究的基础上，安德森等人。[<一个href="#B11">11</一个>]定义了日的所谓“已实现波动”<一世>Ť</一世>如<span class="equation_break" id="EEq15"><span class="left_break" id="L96"></span><span class="middle_break"><span class="center_break" id="M96"> <svg height="37.4764pt" id="M96-1" version="1.1" viewbox="0 0 59.544 37.4764" width="59.544pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B96-1"> <g transform="matrix(.013,0,0,-0.013,0,22.233)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.71,15.969)"> <path d="M397 380C406 395 404 411 396 425S369 451 350 451C302 451 239 372 192 294H189L199 338C214 407 207 451 180 451C152 451 83 405 30 345L48 318C87 354 117 372 125 372S135 362 127 324L55 -5L61 -12C87 -5 117 3 139 5C154 87 168 162 179 207C198 250 240 310 260 332C281 355 297 366 307 366C321 366 333 360 347 346C351 342 360 342 369 348C379 355 389 366 397 380Z" id="g50-115"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,10.6,15.969)"> <path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,6.64,26.017)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.86,22.233)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,32.81,7.468)"> <use xlink:href="#g50-79"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.12,22.239)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,30.41,35.882)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,32.96,35.882)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.52,35.882)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.29,22.233)"> <use xlink:href="#g113-115"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,48.77,15.969)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,48.19,26.017)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.35,26.017)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,53.5,26.017)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.58,22.233)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R96"> <svg class="label" height="11.44pt" id="M96-2" version="1.1" viewbox="0 0 19.288 11.44" width="19.288pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B96-2"> <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,-0.013,8.89,9.26)"> <use xlink:href="#g190-161"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.79,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>在哪里<一世>ñ</一世>一天内等距的间隔数和<svg height="10.3116pt" id="M97" style="vertical-align:-4.35069pt" version="1.1" viewbox="-0.0498162 -5.96091 13.409 10.3116" width="13.409pt" 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="#g113-115"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.059,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.216,3.132)"> <use xlink:href="#g50-106"></use> </g> </svg>日收益率是对数吗<一世>Ť</一世>在时间间隔<一世>一世</一世>与<一世>一世</一世>= 1、2…<一世>ñ</一世>和<一世>Ť</一世>= 1,…,<一世>Ť</一世>。</p> <p>因此，实现波动是平方盘中返回的总和。原则上，让<一世>ñ</一世>倾向于大样本，即连续时间采样，测量方法接近于潜在连续时间过程的真实综合波动率，理论上没有测量误差。此外，这一措施允许市场参与者基本上将波动性视为观察到的变量，并允许直接估计。</p> <h5 id="sec2.4">2.4。预测评估</h5> <h6 id="sec2.4.1">2.4.1。MZ回归</h6> <p>评估波动率模型的样本外预测性能的一种常用方法是<svg height="11.7978pt" id="M98" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 15.4029 11.7978" width="15.4029pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,2.175,0)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.326,-5.741)"> <use xlink:href="#g50-51"></use> </g> </svg>通过mincerz - zarnowitz (MZ)回归，<span class="equation_break" id="EEq16"><span class="left_break" id="L99"></span><span class="middle_break"><span class="center_break" id="M99"> <svg height="16.0778pt" id="M99-1" version="1.1" viewbox="0 0 90.854 16.0778" width="90.854pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B99-1"> <g transform="matrix(.013,0,0,-0.013,0,12.113)"> <use xlink:href="#g113-240"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.35,5.85)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.76,15.897)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.93,12.113)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.19,12.113)"> <path d="M483 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 271 402 301 402C329 402 359 394 374 387Z" id="g113-98"></path> </g> <g transform="matrix(.013,0,0,-0.013,36.68,12.113)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.21,12.113)"> <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,-0.013,53.31,12.113)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,60.02,5.85)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.96,15.897)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,67.87,12.113)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,78.41,12.113)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,84.22,15.245)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,87.89,12.113)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R99"> <svg class="label" height="11.44pt" id="M99-2" version="1.1" viewbox="0 0 19.758 11.44" width="19.758pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B99-2"> <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,-0.013,8.83,9.26)"> <use xlink:href="#g190-227"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.26,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>也就是说，平方收益是对模型预测的回归<svg height="15.535pt" id="M100" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 12.4186 15.535" width="12.4186pt" 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="#g113-240"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.347,-5.741)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.76,3.784)"> <use xlink:href="#g50-117"></use> </g> </svg>和一个常数。在这里,<svg height="15.535pt" id="M101" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 12.4186 15.535" width="12.4186pt" 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="#g113-240"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.347,-5.741)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.76,3.784)"> <use xlink:href="#g50-117"></use> </g> </svg>事后波动(例如，已实现的波动)是否在某个时间<一世>Ť</一世>，<svg height="15.535pt" id="M102" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 11.7792 15.535" width="11.7792pt" 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="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.708,-5.741)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.643,3.784)"> <use xlink:href="#g50-117"></use> </g> </svg>是估计(样本内)还是预测(样本外)的波动<一世>Ť</一世>,<svg height="9.10848pt" id="M103" style="vertical-align:-3.291111pt" version="1.1" viewbox="-0.0498162 -5.81737 9.60008 9.10848" width="9.60008pt" 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="#g185-40"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,5.811,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>为独立同分布的误差项;<svg height="9.10848pt" id="M104" style="vertical-align:-3.291111pt" version="1.1" viewbox="-0.0498162 -5.81737 8.98808 9.10848" width="8.98808pt" 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="#g185-40"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,5.811,3.132)"> <use xlink:href="#g50-106"></use> </g> </svg>〜<一世>ñ</一世>(0,1)。<一世>一个</一世>和<svg height="9.49473pt" id="M105" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt" 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="#g113-99"></use> </g> </svg>是待估计的参数。</p> <p>如果条件方差模型很好地说明，我们应该有<一世>一个</一世>= 0,<svg height="9.49473pt" id="M106" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt" 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="#g113-99"></use> </g> </svg>= 1。根据财务数据序列的具体特征，计算其价值<svg height="11.7978pt" id="M107" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 13.2276 11.7978" width="13.2276pt" 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="#g113-83"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.151,-5.741)"> <use xlink:href="#g50-51"></use> </g> </svg>通常较低(甚至少于5%)[<一个href="#B11">11</一个>]。</p> <h6 id="sec2.4.2">2.4.2条。平均绝对误差</h6> <p>另一种确定估计和预测优度的方法是计算<span class="nowrap"> <svg height="8.80315pt" id="M108" style="vertical-align:-0.04981041pt" version="1.1" viewbox="-0.0498162 -8.75334 28.1545 8.80315" width="28.1545pt" 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="M861 0V28C774 35 771 41 768 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120 35 29 28V0H511C520 31 540 125 546 158L517 162Z" id="g190-70"></path> </g> </svg>。</span>该方法是测量接收到的条件协方差如何接近其相应的实现值。这个公式是<span class="equation_break" id="EEq17"><span class="left_break" id="L109"></span><span class="middle_break"><span class="center_break" id="M109"> <svg height="35.476pt" id="M109-1" version="1.1" viewbox="0 0 116.744 35.476" width="116.744pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B109-1"> <g transform="matrix(.013,0,0,-0.013,0,20.415)"> <use xlink:href="#g190-78"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.58,20.415)"> <use xlink:href="#g190-66"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.57,20.415)"> <use xlink:href="#g190-70"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.69,20.415)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,44.29,11.907)"> <use xlink:href="#g113-50"></use> </g> <rect height="0.65243" width="6.55046" x="44.14" y="16.761"></rect> <g 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<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,-0.013,8.81,9.26)"> <use xlink:href="#g190-223"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.84,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>在哪里<svg height="15.535pt" id="M110" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 12.4186 15.535" width="12.4186pt" 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="#g113-240"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.347,-5.741)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.76,3.784)"> <use xlink:href="#g50-117"></use> </g> </svg>用作代理和<svg height="15.535pt" id="M111" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 11.7792 15.535" width="11.7792pt" 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="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.708,-5.741)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.643,3.784)"> <use xlink:href="#g50-117"></use> </g> </svg>为估计协方差。通过对比<svg height="8.80315pt" id="M112" style="vertical-align:-0.04981041pt" version="1.1" viewbox="-0.0498162 -8.75334 30.3297 8.80315" width="30.3297pt" 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="#g190-78"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.583,0)"> <use xlink:href="#g190-66"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.566,0)"> <use xlink:href="#g190-70"></use> </g> </svg>估计模型之间，它可以给该模型的指示，使最好的估计。</p> <h6 id="sec2.4.3">2.4.3。均方根误差（RMSE）</h6> <p>第三措施是在根均方误差（RMSE），其被定义为<span class="equation_break" id="EEq18"><span class="left_break" 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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></span></span></p> <p>使用这些方法，可以比较估计的模型，并使用相同的测量进行估计和预测，可以确定相对最好的估计模型是否也做出了最好的预测。</p> <h4 id="results-and-discussion">3.结果与讨论</h4> <h5 id="sec3.1">3.1。数据</h5> <p>本文考虑的数据是布伦特原油和咖啡阿拉比卡期货市场的周时间序列，分别以美元/桶和美元/磅表示。这两个系列都包含从彭博社数据库中提取的2005年1月第一周到2016年10月最后一周的数据。全样本分为两部分：样本内数据，用来估计模型参数；样本外数据，用来做预测。样本期为2005年1月第一周至2015年12月最后一周，样本外期为2016年1月第一周至2016年10月最后一周。对于样本外期间，我们还提取了30分钟的日内数据，以实现波动性测量的目的。</p> <h5 id="sec3.2">3.2。平稳性检验和日志返回系列的特点</h5> <p>我们的数据包括两种商品价格:原油和阿拉比卡咖啡。两种商品价格在整个研究期间呈现出相同的趋势和方向。这两种大宗商品的价格从2005年到2008年一直在上涨，从2009年到2010年则以类似的模式下跌。另一个印象是，两个商品级别的系列都是非平稳的(见图)<一个href="//www.newsama.com/journals/jps/2020/1424020/fig1/" target="_blank">1</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="1424020.fig.001" src="https://static-01.hindawi.com/articles/jps/volume-2020/1424020/figures/1424020.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/jps/2020/1424020/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 时间序列图的级别系列，阿拉比卡咖啡和原油。</div> </div> </div> </div> <p>可视化收益率序列为这两个市场，我们描绘图返回时间序列图<一个href="//www.newsama.com/journals/jps/2020/1424020/fig2/" target="_blank">2</一个>。每周收益率序列显示波动持续性，表明大的变化往往是后面的这两个星座和小的变化大的变化往往跟着变化较小，而差分序列表明平稳。该地块的进一步显现，这两种商品的回报率的波动性不仅在选定的样本期间波动聚类现象，而且对他们的收益波动过程有一定的关系。也就是说，当阿拉比卡咖啡价格波动越来越大，原油回报的波动性也成为了大部分的时间大。这是讨论咖啡的价格回报和原油价格收益率的关系的主要动机。</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="1424020.fig.002" src="https://static-01.hindawi.com/articles/jps/volume-2020/1424020/figures/1424020.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/jps/2020/1424020/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 时间序列图为差异系列，阿拉比卡咖啡和原油。</div> </div> </div> </div> <p>表格<一个href="//www.newsama.com/journals/jps/2020/1424020/tab1/" target="_blank">1</一个>分别总结了DF检验两种商品价格水平的结果。从表中可以看出，<span class="nowrap"> <svg height="10.2124pt" id="M114" 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" id="g113-113"></path> </g> </svg>-</span>值大于0.05。因此，单位根的零假设将不被拒绝，即，存在在每个系列的一个单位根问题。</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="3"> <hr></td> </tr> <tr class="thead"> <td class="align_left">系列</Ťd> <td class="align_center"><span class="nowrap"> <svg height="8.02022pt" id="M115" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -7.81382 4.54925 8.02022" width="4.54925pt" 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="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path> </g> </svg>-</span>统计</Ťd> <td class="align_center">麦金农近似<span class="nowrap"> <svg height="10.2124pt" id="M116" 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>价值</Ťd> </tr> <tr> <td class="thead-hr" colspan="3"> <hr></td> </tr> <tr> <td class="align_left">原油</Ťd> <td class="align_center">−1.675</Ťd> <td class="align_center">0.4562</Ťd> </tr> <tr> <td class="align_left">阿拉比卡咖啡</Ťd> <td class="align_center">-2.053</Ťd> <td class="align_center">0.3896</Ťd> </tr> <tr class="table-tr"> <td colspan="3"> <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/jps/2020/1424020/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> DF单位根检验平稳性为价格水平，具有趋势性。</div> </div> </div> </div> <p>如果时间序列数据是不稳定，有必要寻找可能带来的平稳性可能的变换。在实践中，通常是计量经济学家中申报表改造资金的价格。这是因为经常收益率序列被发现是静止的，从而分析是可能的。日志返回系列是由获得<span class="equation_break" id="EEq19"><span class="left_break" id="L117"></span><span class="middle_break"><span class="center_break" id="M117"> <svg height="30.8164pt" id="M117-1" version="1.1" viewbox="0 0 112.394 30.8164" width="112.394pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B117-1"> <g transform="matrix(.013,0,0,-0.013,0,18.162)"> <use xlink:href="#g113-115"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,4.9,21.293)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.2,18.162)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.46,18.162)"> <path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 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transform="matrix(.0091,0,0,-0.0091,87.43,30.519)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,92.99,30.519)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,99.19,18.162)"> <path d="M522 271V272C522 727 399 1134 127 1388L98 1358C311 1139 432 720 432 271C432 -177 308 -597 98 -816L127 -846C399 -597 522 -188 522 271Z" id="g119-158"></path> </g> <g transform="matrix(.013,0,0,-0.013,109.43,18.162)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R117"> <svg class="label" height="11.44pt" id="M117-2" version="1.1" viewbox="0 0 19.598 11.44" width="19.598pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B117-2"> <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,-0.013,8.76,9.26)"> <use xlink:href="#g190-193"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.1,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>在哪里<svg height="9.25202pt" id="M118" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 10.8619 9.25202" width="10.8619pt" 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="#g113-115"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>是实际价格乘以52(这只是一个比例因子)的日志返回序列，以年化，因为我们使用的是每周数据，而每年包含52周，和<svg height="10.2124pt" id="M119" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 11.179 10.2124" width="11.179pt" 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> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>为原价格级数，log为以10为底的自然对数。</p> <p>表格<一个href="//www.newsama.com/journals/jps/2020/1424020/tab2/" target="_blank">2</一个>总结日志收益率序列为每个商品的DF检验。该表显示，这两个<span class="nowrap"> <svg height="10.2124pt" id="M120" 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>值太小(<span class="nowrap"> <svg height="10.2124pt" id="M121" 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>在5%显著性水平下，<0.05)。这说明单位根的零假设在两种情况下都是不成立的。因此，如时间序列图所示，对数返回序列对于每一项都是静止的。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-content fig-content-tab2"> <table class="table-group" id="tab2"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="3"> <hr></td> </tr> <tr class="thead"> <td class="align_left">系列</Ťd> <td class="align_center"><i>Ť</一世>-统计</Ťd> <td class="align_center">麦金农近似<span class="nowrap"> <svg height="10.2124pt" id="M122" 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>价值</Ťd> </tr> <tr> <td class="thead-hr" colspan="3"> <hr></td> </tr> <tr> <td class="align_left">原油</Ťd> <td class="align_center">−5.791</Ťd> <td class="align_center">0.001</Ťd> </tr> <tr> <td class="align_left">阿拉比卡咖啡</Ťd> <td class="align_center">−5.877</Ťd> <td class="align_center">0.001</Ťd> </tr> <tr class="table-tr"> <td colspan="3"> <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2</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jps/2020/1424020/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 日志返回的平稳性的DF单位根检验。</div> </div> </div> </div> <p>看表<一个href="//www.newsama.com/journals/jps/2020/1424020/tab3/" target="_blank">3</一个>，平均价格阿拉比卡咖啡（每英镑）和原油（每桶）分别为$ 145.8668和$ 80.9327，在整个时期。那么平均数收益进行了计算，并且它们分别是0.0458和0.0119咖啡和石油。原油价格的平均收益均高于其在考虑样本期内阿拉比卡咖啡价格回报小。这里还有一个印象是，这两种商品的回归是肯定的，这是两种商品价格呈增长趋势的含义。标准偏差的估计是2.229咖啡和2.3639的油，这是几乎相似。因此，我们可以说，他们表现出他们的价格大致相同的变化。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab3"> <div class="floats-partial-content fig-content-tab3"> <table class="table-group" id="tab3"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="5"> <hr></td> </tr> <tr class="thead"> <td class="align_left" rowspan="2">统计</Ťd> <td class="align_center" colspan="2">咖啡市场</Ťd> <td class="align_center" colspan="2">原油市场</Ťd> </tr> <tr class="thead"> <td class="align_center"><span style="width: 12.6003ptpx;"> <svg height="8.8423pt" id="M123" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 12.6003 8.8423" width="12.6003pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.026,0)"> <path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path> </g> </svg></span></td> <td class="align_center"><span style="width: 8.68666ptpx;"> <svg height="9.25202pt" id="M124" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 8.68666 9.25202" width="8.68666pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g 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transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.026,0)"> <path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path> </g> </svg></span></td> <td class="align_center"><span style="width: 8.68666ptpx;"> <svg height="9.25202pt" id="M126" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 8.68666 9.25202" width="8.68666pt" 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="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"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"> <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"></path> </g> </svg></span></td> </tr> <tr> <td class="thead-hr" colspan="5"> <hr></td> </tr> <tr> <td class="align_left">的意思是</Ťd> <td class="align_center">145.8668</Ťd> <td class="align_center">0.0458</Ťd> <td class="align_center">80.9327</Ťd> <td class="align_center">0.0119</Ťd> </tr> <tr> <td class="align_left">中位数</Ťd> <td class="align_center">132.7250</Ťd> <td class="align_center">0</Ťd> <td class="align_center">76.1950</Ťd> <td class="align_center">0.1327</Ťd> </tr> <tr> <td class="align_left">最大</Ťd> <td class="align_center">299.3500</Ťd> <td class="align_center">9.6800</Ťd> <td class="align_center">144.4900</Ťd> <td class="align_center">10.449</Ťd> </tr> <tr> <td class="align_left">最小值</Ťd> <td class="align_center">88.2000</Ťd> <td class="align_center">−7.538</Ťd> <td class="align_center">28.9400</Ťd> <td class="align_center">-15.451个</Ťd> </tr> <tr> <td class="align_left">Std.dev。</Ťd> <td class="align_center">43.3636</Ťd> <td class="align_center">2.229</Ťd> <td class="align_center">26.1545</Ťd> <td class="align_center">2.3639</Ťd> </tr> <tr> <td class="align_left">偏态</Ťd> <td class="align_center">1.4120</Ťd> <td class="align_center">0.0359</Ťd> <td class="align_center">0.1347</Ťd> <td class="align_center">-0.6890</Ťd> </tr> <tr> <td class="align_left">峰度</Ťd> <td class="align_center">4.4545分</Ťd> <td class="align_center">3.6941</Ťd> <td class="align_center">1.7781</Ťd> <td class="align_center">7.2470</Ťd> </tr> <tr> <td class="align_left">雅克-贝拉</Ťd> <td class="align_center">144.8500 (0.001)</Ťd> <td class="align_center">8.2600 (0.016)</Ťd> <td class="align_center">488.0200（0.001）</Ťd> <td class="align_center">107.4100 (0.001)</Ťd> </tr> <tr class="table-tr"> <td colspan="5"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> <tr class="table-fn"> <td> <div> <svg height="10.1524pt" id="M127" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -10.1025 11.7596 10.1524" width="11.7596pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0091,0,0,-0.0091,0,-5.741)"> <path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 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390 186 422 144C444 143 470 148 486 158Z"></path> </g> </svg>下面的哈尔克 - 贝拉统计值是<span class="nowrap"> <svg height="10.2124pt" id="M128" 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>在显着性水平为5％的值。<br> </div></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表3</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jps/2020/1424020/tab3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 阿拉比卡咖啡和原油系列总结性统计。</div> </div> </div> </div> <h5 id="sec3.3">3.3。波动性建模</h5> <p>要为日志返回序列构建波动率模型，第一步是指定均值方程。一旦我们指定了平均方程，我们必须使用平均方程的残差来测试ARCH效应。如果ARCH效应具有统计学意义，则需要指定波动率模型，并对均值和波动率方程进行联合估计。对于条件波动的GARCH模型，条件均值规范通常是任意的。</p> <h6 id="sec3.3.1">3.3.1。拱效应检验</h6> <p>考虑财务回报模型和拟合这个模型中，如果在每个收益的无波动聚类，随机扰动项<svg height="9.25202pt" id="M129" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 8.79107 9.25202" width="8.79107pt" 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="#g113-247"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,5.005,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>应该是一个白噪声过程。标准化残差图可以作为判断误差项的异方差特征的初步依据。各商品回归序列的标准化残差图如图所示<一个href="//www.newsama.com/journals/jps/2020/1424020/fig3/" target="_blank">3</一个>. 该图描绘了由均值方程生成的两个商品收益率序列的残差图。</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="1424020.fig.003" src="https://static-01.hindawi.com/articles/jps/volume-2020/1424020/figures/1424020.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/jps/2020/1424020/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 利用残差图分析了阿拉比卡咖啡和原油的平均回油序列。</div> </div> </div> </div> <p>从图中可以看出，对于两个系列，都存在一个较长的低波动期和一个较长的高波动期。例如，对于阿拉比卡咖啡的收益，从2005年第一周到2008年底，存在较长时间的低波动，从2014年第一周到2016年年底，存在较长时间的高波动。从2005年第一周到2009年第一周，原油回报率也比咖啡系列表现出较长时间的低波动性。换句话说，高波动期之后往往是高波动期，低波动期之后往往是低波动期，这就是波动率聚类。这表明残差或误差项是有条件异方差的，可以用GARCH模型来表示。</p> <p>表格<一个href="//www.newsama.com/journals/jps/2020/1424020/tab4/" target="_blank">4</一个>显示ARCH LM检验的两个商品返回结果。该表的最后一栏包括<span class="nowrap"> <svg height="10.2124pt" id="M130" 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>表示拒绝原假设的值，即在5%的显著性水平上，直到第四个滞后值“没有ARCH效应”。结果表明，两种商品的价格日志回归序列具有波动性，需要使用GARCH模型进行建模。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab4"> <div class="floats-partial-content fig-content-tab4"> <table class="table-group" id="tab4"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="5"> <hr></td> </tr> <tr class="thead"> <td class="align_left">系列</Ťd> <td class="align_center">奥林匹克广播服务公司<svg height="10.1524pt" id="M131" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -10.1025 6.17869 10.1524" width="6.17869pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0091,0,0,-0.0091,0,-5.741)"> <path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z"></path> </g> </svg> <svg height="11.7978pt" id="M132" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 13.2276 11.7978" width="13.2276pt" 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="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,8.151,-5.741)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path> </g> </svg></td> <td class="align_center"> <svg height="15.2296pt" id="M133" style="vertical-align:-3.6382pt" version="1.1" viewbox="-0.0498162 -11.5914 12.6404 15.2296" width="12.6404pt" 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="M565 434L556 448L482 423L322 189L287 373C280 410 261 448 236 448C207 448 161 415 110 338L131 317C160 355 181 374 193 374C204 374 208 366 217 330C230 279 247 185 259 116L50 -175C18 -223 29 -260 41 -278H51C97 -198 207 -33 270 57L313 -165C328 -235 349 -261 376 -261S445 -244 510 -150L487 -127C444 -178 423 -186 411 -186C402 -186 398 -177 387 -130C371 -62 349 39 332 135C390 217 524 392 565 434Z"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,7.568,-5.741)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path> </g> </svg>(4)</Ťd> <td class="align_center">滞后(<span class="nowrap"> <svg height="10.2124pt" id="M134" 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">概率。</Ťd> </tr> <tr> <td class="thead-hr" colspan="5"> <hr></td> </tr> <tr> <td class="align_left">阿拉比卡咖啡</Ťd> <td class="align_center">12.6477</Ťd> <td class="align_center">9.488</Ťd> <td class="align_center">4</Ťd> <td class="align_center">0.004</Ťd> </tr> <tr> <td class="align_left">原油</Ťd> <td class="align_center">105.6419</Ťd> <td class="align_center">9.488</Ťd> <td class="align_center">4</Ťd> <td class="align_center">0.001</Ťd> </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4</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jps/2020/1424020/tab4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> ARCH LM测试汇总统计。</div> </div> </div> </div> <h5 id="sec3.4">3.4。多元GARCH模型</h5> <p>在审查多元GARCH模型的不同配方的开始，应该考虑什么是多元GARCH模型的规范应在对比的是单变量情况下的罚款。在一方面，它应该是灵活的，足以说明条件方差和协方差的动态。在另一方面，作为参数在多元GARCH模型的增加与模型的尺寸迅速沿号码，确定应该吝啬简化模型估计也达到了模型参数的简单解释的目的。然而，简约性可以减少参数的数量，在这种情况中的协方差矩阵的相关动力学不能被捕获。</p> <p>在相关文献中，大量使用了不同的MGARCH公式对长期条件异方差进行建模。最广泛使用的是时变条件相关(VCC)、常数条件相关(CCC)和动态条件相关(DCC)模型[<一个href="#B5">五</一个>]。这些模型的更详尽的讨论见第二章的section2.1。一个多元GARCH模型的复杂性在于参数的数量迅速增加和研究人员经常使用的型号规格单ARCH和GARCH项，而且往往是足够捕捉的变化。因此，在本文中，我们使用二元-GARCH（1,1）模型。</p> <p>一本研究的主要目的是选择从竞争车型适当的多元GARCH模型。使用明瑟，Zarnowitz回归和预测误差的措施，以最小的预测误差测量值和最大MZ模型<svg height="11.7978pt" id="M135" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 13.2276 11.7978" width="13.2276pt" 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="#g113-83"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.151,-5.741)"> <use xlink:href="#g50-51"></use> </g> </svg>值被选择为适当的模型。我们可以选择一个二元GARCH模型，然后估计所选择的模型的参数。对于创新项的分布，多元正态分布和学生的多元版本<一世>Ť</一世>考虑了八自由度的分布。和前面的分析一样，我们也考虑了两个波动率指标，即周收益率平方和30分钟日内收益率平方。</p> <p>看表<一个href="//www.newsama.com/journals/jps/2020/1424020/tab5/" target="_blank">五</一个>和<一个href="//www.newsama.com/journals/jps/2020/1424020/tab6/" target="_blank">6</一个>对于每个模型，<一世>[R</一世><sup>2</sup>从明塞尔-Zarnowitz回归获得（<一世>[R</一世><sup>2</sup>)，高频数据值较大。此外,<一世>[R</一世><sup>2</sup>是学生在大<一世>Ť</一世>创新项的分布假设。现在结合高频数据和学生<一世>Ť</一世>对于阿拉比卡咖啡收益和原油收益的方差协方差估计，时变条件相关(VCC)模型是一种较好的模型。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab5"> <div class="floats-partial-content fig-content-tab5"> <table class="table-group" id="tab5"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="7"> <hr></td> </tr> <tr class="thead"> <td class="align_left" rowspan="3">统计</Ťd> <td class="align_center" colspan="6">实现波动率测量</Ťd> </tr> <tr class="thead"> <td class="align_center" colspan="3">每周回报率的平方</Ťd> <td class="align_center" colspan="3">30分钟间隔返回(高频率)。</Ťd> </tr> <tr class="thead"> <td class="align_center">CCC</Ťd> <td class="align_center">DCC</Ťd> <td class="align_center">VCC</Ťd> <td class="align_center">CCC</Ťd> <td class="align_center">DCC</Ťd> <td class="align_center">VCC</Ťd> </tr> <tr> <td class="thead-hr" colspan="7"> <hr></td> </tr> <tr> <td class="align_left">MZ.reg.R2</Ťd> <td class="align_center">0.0145</Ťd> <td class="align_center">0.0037</Ťd> <td class="align_center">0.0070</Ťd> <td class="align_center">0.2575</Ťd> <td class="align_center">0.1740</Ťd> <td class="align_center">0.3929</Ťd> </tr> <tr> <td class="align_left">均方误差</Ťd> <td class="align_center">29.2503</Ťd> <td class="align_center">29.9553</Ťd> <td class="align_center">29.313629</Ťd> <td class="align_center">0.7865</Ťd> <td class="align_center">0.9161</Ťd> <td class="align_center">0.8590个</Ťd> </tr> <tr> <td class="align_left">RMSE</Ťd> <td class="align_center">5.1442</Ťd> <td class="align_center">5.4730</Ťd> <td class="align_center">5.4083</Ťd> <td class="align_center">0.8868</Ťd> <td class="align_center">0.9571</Ťd> <td class="align_center">0.9268</Ťd> </tr> <tr> <td class="align_left">梅</Ťd> <td class="align_center">3.7900</Ťd> <td class="align_center">3.7452</Ťd> <td class="align_center">3.7307</Ťd> <td class="align_center">0.879</Ťd> <td class="align_center">0.8517</Ťd> <td class="align_center">0.8000</Ťd> </tr> <tr> <td class="align_left">AIC公司</Ťd> <td class="align_center">4965.981</Ťd> <td class="align_center">4957.583</Ťd> <td class="align_center">4962.655</Ťd> <td class="align_center">4965.981</Ťd> <td class="align_center">4962.655</Ťd> <td class="align_center">4957.583</Ťd> </tr> <tr> <td class="align_left">BIC</Ťd> <td class="align_center">5022.474</Ťd> <td class="align_center">5022.768</Ťd> <td class="align_center">5027.84</Ťd> <td class="align_center">5022.474</Ťd> <td class="align_center">5022.768</Ťd> <td class="align_center">5027.84</Ťd> </tr> <tr> <td class="align_left">噢</Ťd> <td class="align_center">-2469.99</Ťd> <td class="align_center">−2463.79</Ťd> <td class="align_center">−2466.32</Ťd> <td class="align_center">-2469.99</Ťd> <td class="align_center">−2463.79</Ťd> <td class="align_center">−2466.32</Ťd> </tr> <tr class="table-tr"> <td colspan="7"> <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5</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jps/2020/1424020/tab5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 正态分布下的二元GARCH模型的咖啡和油品收益共波动率的比较。</div> </div> </div> </div> <div class="floats-partial-section partial-other-wrapper" data-section="tab6"> <div class="floats-partial-content fig-content-tab6"> <table class="table-group" id="tab6"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="7"> <hr></td> </tr> <tr class="thead"> <td class="align_left" rowspan="3">统计</Ťd> <td class="align_center" colspan="6">实现波动率测量</Ťd> </tr> <tr class="thead"> <td class="align_center" colspan="3">每周返回广场</Ťd> <td class="align_center" colspan="3">高频率</Ťd> </tr> <tr class="thead"> <td class="align_center">CCC</Ťd> <td class="align_center">DCC</Ťd> <td class="align_center">VCC</Ťd> <td class="align_center">CCC</Ťd> <td class="align_center">DCC</Ťd> <td class="align_center">VCC</Ťd> </tr> <tr> <td class="thead-hr" colspan="7"> <hr></td> </tr> <tr> <td class="align_left">MZ.reg.R2</Ťd> <td class="align_center">0.0937</Ťd> <td class="align_center">0.0747号</Ťd> <td class="align_center">0.060</Ťd> <td class="align_center">0.2372</Ťd> <td class="align_center">0.1614</Ťd> <td class="align_center">0.4014</Ťd> </tr> <tr> <td class="align_left">均方误差</Ťd> <td class="align_center">29.36</Ťd> <td class="align_center">29.99</Ťd> <td class="align_center">29.28</Ťd> <td class="align_center">0.7876</Ťd> <td class="align_center">0.8877</Ťd> <td class="align_center">0.8634</Ťd> </tr> <tr> <td class="align_left">RMSE</Ťd> <td class="align_center">5.4184条</Ťd> <td class="align_center">5.4763</Ťd> <td class="align_center">5.4110</Ťd> <td class="align_center">0.8874</Ťd> <td class="align_center">0.9421个</Ťd> <td class="align_center">0.9291</Ťd> </tr> <tr> <td class="align_left">梅</Ťd> <td class="align_center">3.7953</Ťd> <td class="align_center">3.7532</Ťd> <td class="align_center">3.742</Ťd> <td class="align_center">0.8819</Ťd> <td class="align_center">0.8423</Ťd> <td class="align_center">0.8372</Ťd> </tr> <tr> <td class="align_left">AIC公司</Ťd> <td class="align_center">4945.74</Ťd> <td class="align_center">4940.492</Ťd> <td class="align_center">4943.54</Ťd> <td class="align_center">4945.74</Ťd> <td class="align_center">4943.54</Ťd> <td class="align_center">4940.492</Ťd> </tr> <tr> <td class="align_left">BIC</Ťd> <td class="align_center">5002.24</Ťd> <td class="align_center">5005.677个</Ťd> <td class="align_center">5008.725</Ťd> <td class="align_center">5002.24</Ťd> <td class="align_center">5005.677个</Ťd> <td class="align_center">5008.725</Ťd> </tr> <tr> <td class="align_left">噢</Ťd> <td class="align_center">−2459.84</Ťd> <td class="align_center">−2455.24</Ťd> <td class="align_center">−2456.77</Ťd> <td class="align_center">−2459.84</Ťd> <td class="align_center">−2455.24</Ťd> <td class="align_center">−2456.77</Ťd> </tr> <tr class="table-tr"> <td colspan="7"> <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6</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jps/2020/1424020/tab6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 二元GARCH根据学员的模式比较<一世>Ť</一世>咖啡和油品收益的共波动性分布。</div> </div> </div> </div> <p>结果见表<一个href="//www.newsama.com/journals/jps/2020/1424020/tab7/" target="_blank">7</一个>的方差方程实际上表明波动率效应在整个样本周期的回报系列考虑。关于时变相关性的估计<span class="nowrap"> <svg height="13.5431pt" id="M136" style="vertical-align:-4.25477pt" version="1.1" viewbox="-0.0498162 -9.28833 48.324 13.5431" width="48.324pt" 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,-0.013,6.057,-.222)"> <path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z" id="g119-17"></path> </g> <g transform="matrix(.013,0,0,-0.013,4.498,0)"> <use xlink:href="#g113-239"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.66,3.132)"> <path d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 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transform="matrix(.0091,0,0,-0.0091,24.064,3.132)"> <path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z" id="g190-102"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,27.977,3.132)"> <use xlink:href="#g190-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.789,3.132)"> <path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z" id="g190-45"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,33.864,3.132)"> <use xlink:href="#g190-112"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.396,3.132)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,40.88,3.132)"> <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="g190-109"></path> </g> <g transform="matrix(.013,0,0,-0.013,43.826,0)"> <use xlink:href="#g113-42"></use> </g> </svg>，</span>相关被认为是积极的和显著。这意味着有条件的波动两个串联商品系列之间的正相关关系，并表示对这些商品的回报休戚与共。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab7"> <div class="floats-partial-content fig-content-tab7"> <table class="table-group" id="tab7"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr class="thead"> <td class="align_left">参数</Ťd> <td class="align_center">系数</Ťd> <td class="align_center"><i>ž</一世>统计数据</Ťd> <td class="align_center"><span class="nowrap"> <svg height="10.2124pt" id="M138" 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>价值</Ťd> </tr> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr> <td class="align_left"><span style="width: 29.8608ptpx;"> <svg height="12.522pt" id="M139" style="vertical-align:-3.27279pt" version="1.1" viewbox="-0.0498162 -9.24921 29.8608 12.522" width="29.8608pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.683,-.222)"> <path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,7.969,3.132)"> <path d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,11.818,3.132)"> <path d="M257 449C165 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116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,25.286,3.132)"> <path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z"></path> </g> </svg></span></td> <td class="align_center">0.1647</Ťd> <td class="align_center">1.04</Ťd> <td class="align_center">0.300</Ťd> </tr> <tr> <td class="align_left"><span style="width: 28.9474ptpx;"> <svg height="12.522pt" id="M140" style="vertical-align:-3.27279pt" version="1.1" viewbox="-0.0498162 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312V106C102 38 95 32 32 26V0H252Z"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,44.623,3.132)"> <path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z"></path> </g> </svg></span></td> <td class="align_center">0.9866</Ťd> <td class="align_center">-</Ťd> <td class="align_center">-</Ťd> </tr> <tr class="table-tr"> <td colspan="4"> <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7</span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jps/2020/1424020/tab7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 从随时间变化的条件相关性（VCC-GARCH）模型下方差的参数估计<一世>Ť</一世>分配(<span class="nowrap"> <svg height="8.58131pt" id="M137" style="vertical-align:-0.2324905pt" version="1.1" viewbox="-0.0498162 -8.34882 27.1713 8.58131" width="27.1713pt" 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="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,9.495,0)"> <path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path> </g> <g transform="matrix(.013,0,0,-0.013,20.758,0)"> <path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z"></path> </g> </svg>).</span> </div> </div> </div> </div> <p>参数的估计<svg height="12.4307pt" id="M150" style="vertical-align:-3.18149pt" version="1.1" viewbox="-0.0498162 -9.24921 11.79 12.4307" width="11.79pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.116,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.358,3.132)"> <use xlink:href="#g50-50"></use> </g> </svg>和<span class="nowrap"> <svg height="12.4307pt" id="M151" style="vertical-align:-3.18149pt" version="1.1" viewbox="-0.0498162 -9.24921 14.9331 12.4307" width="14.9331pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,.65,-.222)"> <use xlink:href="#g119-105"></use> </g> <g transform="matrix(.013,0,0,-0.013,2.175,0)"> <use xlink:href="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.887,3.132)"> <use xlink:href="#g50-51"></use> </g> </svg>，</span>即，处理在当前的动态条件的相关性以前冲击和先前动态相关性的效果的参数，来自零显著不同，与<svg height="12.4307pt" id="M152" style="vertical-align:-3.18149pt" version="1.1" viewbox="-0.0498162 -9.24921 11.79 12.4307" width="11.79pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.116,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.358,3.132)"> <use xlink:href="#g50-50"></use> </g> </svg> = 0.0291 and<svg height="12.4307pt" id="M153" style="vertical-align:-3.18149pt" version="1.1" viewbox="-0.0498162 -9.24921 11.79 12.4307" width="11.79pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.116,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.358,3.132)"> <use xlink:href="#g50-51"></use> </g> </svg>= 0.919。时，时变条件相关(VCC)模型退化为不变条件相关(CCC)模型<svg height="12.4307pt" id="M154" style="vertical-align:-3.18149pt" version="1.1" viewbox="-0.0498162 -9.24921 60.694 12.4307" width="60.694pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.116,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.358,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.964,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.342,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.227,0)"> <use xlink:href="#g113-238"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,34.585,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.191,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,54.454,0)"> <use xlink:href="#g113-49"></use> </g> </svg>[<一个href="#B1">1</一个>]。因此，采用CCC的限制太大，这些系列。</p> <p>关于持久性的估计(<span class="nowrap"> <svg height="16.0061pt" id="M155" style="vertical-align:-3.4295pt" version="1.1" viewbox="-0.0498162 -12.5766 33.359 16.0061" width="33.359pt" 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)"> <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(.0091,0,0,-0.0091,7.059,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.047,0)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.938,-3.549)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.583,0)"> <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(.0091,0,0,-0.0091,30.811,3.132)"> <use xlink:href="#g50-106"></use> </g> </svg>),</span>持久性估计是0.9698和0.9866，在咖啡和石油市场，分别是接近1，这意味着波动是在这些市场中持续。为方差矩阵的充分条件是正定是通常GARCH限制，即<svg height="12.7178pt" id="M156" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 59.2634 12.7178" width="59.2634pt" 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="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z" id="g113-246"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.295,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.614,0)"> <use xlink:href="#g113-223"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.999,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.317,0)"> <use xlink:href="#g113-224"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.503,0)"> <path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z" id="g117-92"></path> </g> <g transform="matrix(.013,0,0,-0.013,52.766,0)"> <use xlink:href="#g113-49"></use> </g> </svg>对于单变量GARCH（1，1）模型。而且，这个单变量GARCH过程需要是平稳的，即。，<svg height="12.7178pt" id="M157" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 50.4724 12.7178" width="50.4724pt" 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="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.145,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,19.682,0)"> <use xlink:href="#g113-223"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.973,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.684,0)"> <use xlink:href="#g113-224"></use> </g> </svg>> 0。这些条件在上面的输出表中得到了满足。</p> <h5 id="sec3.5">3.5。讨论</h5> <p>其目的一直是建模和预测的使用二元GARCH模型布伦特原油和阿拉比卡咖啡期货市场收盘价为每周时间序列covolatility动态。来自考虑的时间段初步分析，这两个价格序列呈现递增的趋势。为了确定是否系列是静止的或没有，增强迪基一富勒（ADF）试验进行。通常情况下，大宗商品价格的原始数据是不稳定，这也是本研究的情况。对于这两种电平的时间系列，测试表明，以单位根I（1）的存在。每个时间序列的第一个日志差异被认为是固定的（表<一个href="//www.newsama.com/journals/jps/2020/1424020/tab3/" target="_blank">3</一个>).</p> <p>在这两种商品的回报率中，ARCH项系数在5%的显著性水平上是显著的。结果是波动性聚类的存在，即大变化后大变化，小变化后小变化。</p> <p>诺埃米和朱尼尔[<一个href="#B12">12</一个>]研究了两种热带商品，即世界咖啡和原油的波动性，并发现这两种商品的易变性，得出的结论是在咖啡和可可价格波动追随石油价格的波动。我们的研究结果表明，阿拉比卡咖啡和原油波动是相关的（其实不高）。此外，阿拉比卡咖啡和原油的协方差被发现是类似于原油的方差这表明在阿拉比卡咖啡价格的变化如下原油价格，类似的发现与诺埃米和小型。</p> <p>总体而言，这些商品收益之间的正相关关系与以往关于能源与商品共波动性的研究一致(如，[<一个href="#B13">13</一个>，<一个href="#B14">14</一个>]）。</p> <h4 id="conclusion-and-recommendations">4.结论和建议</h4> <p>预测资产回报的波动动态一直是学者、从业者和投资组合经理广泛研究的主题。本文估计各种多元GARCH模型使用周收盘价格(美元/桶)布伦特原油和周收盘价格(美元/每磅)的阿拉比卡咖啡并比较这些模型的预测性能盘中基于高频数据允许更精确的实现波动率测量。分析结果表明，不同条件相关(VCC)模型与学生学习成绩之间存在显著的相关关系<一世>Ť</一世>在我们的经验背景下，分布式创新术语是最精确的波动预测模型。</p> <p>我们建议并鼓励未来研究MGARCH模型预测性能的研究人员特别注意已实现波动的测量，在可行的情况下使用高频数据。</p> <p>我们也建议有兴趣预见这两大商品的价格波动在埃塞俄比亚经济的背景下，公共政策的制定者考虑使用因为它是基于一些强大的计量工作，并高度评价这项研究是在审议输入记录的信息相应的数据。</p> <p>本研究的分析范围仅限于两种商品之间的协波动性。为了克服这一限制并提供更细致的分析，未来的研究人员可能会考虑将股票、货币和债券市场的波动纳入分析。尽管这一研究议程可能很复杂，但鉴于近年来全球金融市场和商品市场之间更深入的一体化，其结果可能是有益的，这一现象后来被称为商品金融化。</p> <h4 id="data-availability">数据可用性</h4> <p>支持研究结果的数据可根据要求从通信作者处获得。</p> <h4 id="conflicts-of-interest">的利益冲突</h4> <p>作者声明本论文的发表不存在利益冲突。</p> </div> <div class="xml-content"> <h4 class="references" id="references">参考文献</h4> <ol> <li id="B1">L.鲍文斯，C.哈夫纳和S.劳伦特，《波动率模型》<一世>波动率模型及其应用手册</一世>， L. 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Hayes&publication_year=2011" target="_blank">谷歌学术</一个></span></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</h4> <p>版权所有©2020达维特Yeshiwas和Yebelay Berelie。这是下发布的开放式访问文章<一个rel="license" href="http://creativecommons.org/licenses/by/4.0/">知识共享署名许可</一个>，它允许在任何媒体中不受限制地使用、分发和复制，前提是正确引用了原始作品。</p> </div> </div> </article> </div> </div> </div> <div class="biblio__Wrapper-sc-1nou1lz-0 eyHfWh journal_article__BiblioIntegratorWidget-sc-12fk6zy-6 bqUtxN article_widget biblioWrapper hide"> <hr> <h4 class="biblio__H4-sc-1nou1lz-2 pYnJQ hrTitleRef">更多相关文章</h4> <div id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 iuAHWW"></div> </div> </div> </div> <div class="threeColumn__RightWrapper-sc-1bf4078-2 sZeeW rightWrapper"> <div id="rightSectionMenu" class="sc-hZSUBg hwTmaF journal_article__StickyRight-sc-12fk6zy-0 xuPEv"> <div class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-1 iKpUSJ article_sticky_top_toolbar"> <div class="sc-jrIrqw deaPpH 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src="data:image/svg+xml;base64,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" height="24"><span class="text">下载引用</span></span><img alt="" class="sc-EHOje ggEPYc sc-fYiAbW eBEQa fileArrow" title="" role="presentation" src="data:image/svg+xml;base64,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" height="20"></a> <a class="sc-htpNat bUhGXt link sc-cbkKFq dNPgJJ sc-fHxwqH dPWBKK ref_desktop" href="//www.newsama.com/journals/jps/2020/1424020.ris" aria-label="" target="" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje fEOMwM sc-krvtoX isUmzT" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="text">引用</span></span><img alt="" class="sc-EHOje ggEPYc sc-fYiAbW eBEQa fileArrow" title="" role="presentation" src="data:image/svg+xml;base64,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" height="20"></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-12fk6zy-2 gvAMNw article_sticky_bottom_toolbar"> <div class="sc-fyjhYU bmCmNg article_bottom_toolbar"> <div class="sc-ugnQR bdNavy accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje fEOMwM sc-iomxrj czMNsj" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="sc-iFMziU gCiAsp">下载其他格式</span><span class="sc-keVrkP hYjHxB">更多</span></span> <img alt="" class="sc-EHOje fEOMwM sc-dvCyap bivFoZ" title="" role="presentation" 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src="data:image/svg+xml;base64,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" height="14">作者</一个></li> <li><a class="sc-htpNat bUhGXt link editors" href="//www.newsama.com/publish-research/editors/" aria-label="Editors"><img alt="" class="sc-EHOje jRIjVn" title="" role="presentation" src="data:image/svg+xml;base64,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" height="14">编者</一个></li> <li><a class="sc-htpNat bUhGXt link reviewers" href="//www.newsama.com/publish-research/reviewers/" aria-label="Reviewers"><img alt="" class="sc-EHOje jRIjVn" title="" role="presentation" src="data:image/svg+xml;base64,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" 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src="data:image/svg+xml;base64,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" height="14">雷电竞APP</a></li> <li><a class="sc-htpNat bUhGXt link open_archives_initiative" href="//www.newsama.com/open-archives-initiative/" aria-label="Open Archives Initiative"><img alt="" class="sc-EHOje jRIjVn" title="" role="presentation" src="data:image/svg+xml;base64,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" height="14">开放档案计划</一个></li> </ul> </nav> <div class="sc-ckVGcZ gizesk 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