Collective Origin of the Coexistence of Apparent RMT Noise and Factors in Large Sample Correlation Matrices
arXiv:cond-mat/0210115 · doi:10.1016/j.physa.2003.09.004
Abstract
Through simple analytical calculations and numerical simulations, we demonstrate the generic existence of a self-organized macroscopic state in any large multivariate system possessing non-vanishing average correlations between a finite fraction of all pairs of elements. The coexistence of an eigenvalue spectrum predicted by random matrix theory (RMT) and a few very large eigenvalues in large empirical correlation matrices is shown to result from a bottom-up collective effect of the underlying time series rather than a top-down impact of factors. Our results, in excellent agreement with previous results obtained on large financial correlation matrices, show that there is relevant information also in the bulk of the eigenvalue spectrum and rationalize the presence of market factors previously introduced in an ad hoc manner.
4 pages with 3 figure
References in corpus (6)
- A Random Matrix Approach to Cross-Correlations in Financial Data
- Statistics of Atmospheric Correlations
- A New Method to Estimate the Noise in Financial Correlation Matrices
- Towards identifying the world stock market cross-correlations: DAX versus Dow Jones
- Data clustering and noise undressing for correlation matrices
- Measures of globalization based on cross-correlations of world financial indices
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- Random selection of factors preserves the correlation structure in a linear factor model to a high degree
- Universality results for largest eigenvalues of some sample covariance matrix ensembles
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- Generic Features in the Spectral Decomposition of Correlation Matrices