The measured correlations of financial time series in subsequent epochs change considerably as a function of time. When studying the whole correlation matrices, quasi-stationary patterns, referred to as market states, are seen by applying clustering methods. They emerge, disappear or reemerge, but they are dominated by the collective motion of all stocks. In the jargon, one speaks of the market motion, it is always associated with the largest eigenvalue of the correlation matrices. Thus the question arises, if one can extract more refined information on the system by subtracting the dominating market motion in a proper way. To this end we introduce a new approach by clustering reduced-rank correlation matrices which are obtained by subtracting the dyadic matrix belonging to the largest eigenvalue from the standard correlation matrices. We analyze daily data of 262 companies of the S&P 500 index over a period of almost 15 years from 2002 to 2016. The resulting dynamics is remarkably different, and the corresponding market states are quasi-stationary over a long period of time. Our approach adds to the attempts to separate endogenous from exogenous effects.

中文翻译：

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揭示与集体市场运动相关的相关结构的动态

在随后的时期中，金融时间序列的测量相关性随时间发生了显着变化。在研究整个相关矩阵时，通过应用聚类方法可以看到称为市场状态的准平稳模式。它们出现、消失或重新出现，但它们受所有股票的集体运动支配。用行话来说，市场运动总是与相关矩阵的最大特征值相关联。因此出现了一个问题，是否可以通过以适当的方式减去主导市场运动来提取有关系统的更精细的信息。为此，我们引入了一种新方法，通过聚类降秩相关矩阵，这些矩阵是通过从标准相关矩阵中减去属于最大特征值的二进矩阵而获得的。我们分析了标准普尔 500 指数 262 家公司在 2002 年至 2016 年近 15 年的每日数据。由此产生的动态显着不同，相应的市场状态在很长一段时间内是准平稳的。我们的方法增加了将内生效应与外生效应分开的尝试。