Schäfer Rudi, Seligman Thomas H
Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca, México.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Sep;88(3):032115. doi: 10.1103/PhysRevE.88.032115. Epub 2013 Sep 10.
Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used, this implies an analysis of highly singular correlation matrices. We attack this problem by using the so-called power map, which was introduced to reduce noise. Its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so-emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.
相关矩阵是分析一般复杂系统，尤其是金融市场时间演化的标准工具。然而，大多数分析都假定基础时间序列是平稳的。这往往是一个有效性各异且常常存疑的假设。随着使用的时间序列变短，该假设的有效性会提高。如果使用多个时间序列，这意味着要分析高度奇异的相关矩阵。我们通过使用所谓的幂映射来解决这个问题，幂映射是为了减少噪声而引入的。它的非线性打破了零特征值的简并性，并且我们分析由此产生的谱对相关性的敏感度。这种敏感度将在不相关和相关的威沙特系综中得到证明。
