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摘要翻译：
协方差矩阵是在一个具有长记忆的线性多元ARCH过程的框架下建立的，其中协方差的自然交叉积结构是通过增加两个具有各自参数的线性项来推广的。利用历史数据和协方差矩阵（平方根的逆）计算线性ARCH过程的残差。提出了评价残差分布独立性和单位幅值的简单质量测度。对于大小为54、55和330的三个数据集，研究了计算残差的显著性质。在协方差中引入的两个新项都有助于产生不相关的残差，但残差大小与单位有很大不同。当时间序列数目较大时，从经验数据中提取的信息有限，从而导致推断残差的大小较大，这意味着推断的基本局限性。
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英文标题：
《Inference on multivariate ARCH processes with large sizes》
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作者：
Gilles Zumbach
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最新提交年份：
2009
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective parameter. The residuals of the linear ARCH process are computed using historical data and the (inverse square root of the) covariance matrix. Simple measure of qualities assessing the independence and unit magnitude of the residual distributions are proposed. The salient properties of the computed residuals are studied for three data sets of size 54, 55 and 330. Both new terms introduced in the covariance help in producing uncorrelated residuals, but the residual magnitudes are very different from unity. The large sizes of the inferred residuals are due to the limited information that can be extracted from the empirical data when the number of time series is large, and denotes a fundamental limitation to the inference that can be achieved.
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PDF链接：
https://arxiv.org/pdf/0903.1531
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