Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series

By V. Plerou, P. Gopikrishnan, Bernd Rosenow, L. A. Amaral, H. Eugene Stanley. 1999

We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a few of the largest eigenvalues. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices. Furthermore, we analyze the eigenvectors of C through their inverse participation ratio and find eigenvectors with large inverse participation ratios at both edges of the eigenvalue spectrum--a situation reminiscent of results in localization theory.

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Citations in the corpus

Nonlinear bivariate dependency of price–volume relationships in agricultural commodity futures markets: A perspective from Multifractal Detrended Cross-Correlation Analysis (2011, methodology): “applied methods of randommatrix theory to analyze the cross-correlation matrix of price changes in the largest 1000 US stocks [9].”
Estimating High Dimensional Covariance Matrices and its Applications (2011, background): “All eigenvalues are bounded by λmax in the limit; see Laloux et al. (1999), Plerou et al. (1999), Z. Bai (1999), and the reference therein.”
Econophysics: Empirical facts and agent-based models (2009, unknown): “Cross-correlations in financial data were also studied by Plerou et al. (1999, 2002).”
Cluster analysis for portfolio optimization (2005, methodology): “…uncertainty (in the econophysics literature the term of noise dressing has been used) (Galluccio et al., 1998; Laloux et al., 1999, 2000; Plerou et al., 1999, 2002; Gopikrishnan et al., 2001; Drozdz et al., 2001; Rosenow et al., 2002; Pafka and Kondor, 2003, 2004; Rosenow et al., 2003;…”
Correlation structure and dynamics in volatile markets (2010, background): “Given that the authors of [7, 8] have studied a rather similar set of data, but over the period 1991–1996, we might conclude that something has changed in the market’s correlation structure since 1996.”