Collective origin of the coexistence of apparent random matrix theory noise and of factors in large sample correlation matrices
✍ Scribed by Y. Malevergne; D. Sornette
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 287 KB
- Volume
- 331
- Category
- Article
- ISSN
- 0378-4371
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✦ Synopsis
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 ÿnite 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 bottomup collective e ect of the underlying time series rather than a top-down impact of factors. Our results, in excellent agreement with previous results obtained on large ÿnancial 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.