Random matrix approach to cross correlations in financial data.

By V. Plerou, P. Gopikrishnan, Bernd Rosenow, L. A. Amaral, T. Guhr, H. Eugene Stanley. Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

898 citations recorded by the source corpus.

We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994-1995, (ii) 30-min returns of 881 US stocks for the 2-yr period 1996-1997, and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962-1996. We test the statistics of the eigenvalues lambda(i) of C against a "null hypothesis"--a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [lambda(-),lambda(+)] for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matrices-implying a large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. In addition, we find that these "deviating eigenvectors" are stable in time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Finally, we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return.

Subfields: Condensed Matter Physics, Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/60f18f5e9b0be456033ffe9f73c4999fb8327ac1

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Citations in the corpus

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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;…”
Random Matrix Theory and Fund of Funds Portfolio Optimisation (2007, methodology): “The spectral properties ofCmay be compared to those of a “random”Wishart correlation matrix [8,11],”
Econophysics: Empirical facts and agent-based models (2009, neutral): “Cross-correlations in financial data were also studied by Plerou et al. (1999, 2002).”
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ESTIMATION OF SPIKED EIGENVALUES IN SPIKED MODELS (2012, background): “In practice, some extreme sample eigenvalues are well separated from the bulk eigenvalues for certain type of data, such as speech recognition [11, 15], mathematical finance [20, 21, 26], wireless communication [30], physics of mixture [27], and data analysis and statistical learning [13].”
The Fitness Landscape of HIV-1 Gag: Advanced Modeling Approaches and Validation of Model Predictions by In Vitro Testing (2014, result): “In analogy with past studies on the economic markets and enzymes [13–15], we termed these groups of residues ‘‘sectors’’.”
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On the analysis of cross-correlations in South African market data (2004, methodology): “In [ 28 ], it was found that the largest four eigenvectors obtained from high-frequency data (returns at 30-min intervals) were stable up to time-lags of 1 year, while the largest two eigenvectors from 30 years of daily data were stable for time-scales up to 20 years.”
Droplet barcoding for single cell transcriptomics applied to embryonic stem cells (2015, neutral): “5E), which are not explained by independent fluctuations in each gene (Marčenko and Pastur, 1967; Plerou et al. 2002).”
Eigenvalues of large sample covariance matrices of spiked population models (2004, background): “The examples include speech recognition [6, 12] , mathematical finance [18], [13], [14], wireless communication [25], physics of mixture [19], and data analysis and statistical learning [10].”