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摘要翻译：
研究了三个数据集54、55和330的大经验协方差和相关矩阵的显着性质。协方差被定义为收益的简单交叉积，权重以对数缓慢衰减。协方差矩阵的主要一般性质如下。协方差谱是非常静态的，除了前三到十个特征值外，并迅速向零指数衰减。平均谱和谱密度没有显示出将“有意义的”特征值与“有噪声的”特征值分开的特殊特征。相关性的谱更静态，有三到五个特征值具有明显的动力学。前导子空间上秩k的平均投影显示，大多数动力学发生在特征向量中，包括谱的深处。总之，这意味着协方差减少到几个领先的本征模会错过大部分动力学，协方差估计器可以正确地评估挥发度和相关性。
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英文标题：
《The empirical properties of large covariance matrices》
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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 salient properties of large empirical covariance and correlation matrices are studied for three datasets of size 54, 55 and 330. The covariance is defined as a simple cross product of the returns, with weights that decay logarithmically slowly. The key general properties of the covariance matrices are the following. The spectrum of the covariance is very static, except for the top three to ten eigenvalues, and decay exponentially fast toward zero. The mean spectrum and spectral density show no particular feature that would separate "meaningful" from "noisy" eigenvalues. The spectrum of the correlation is more static, with three to five eigenvalues that have distinct dynamics. The mean projector of rank k on the leading subspace shows instead that most of the dynamics occur in the eigenvectors, including deep in the spectrum. Together, this implies that the reduction of the covariance to a few leading eigenmodes misses most of the dynamics, and that a covariance estimator correctly evaluates both volatilities and correlations.
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PDF链接：
https://arxiv.org/pdf/0903.1525
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