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Collective Origin of the Coexistence of Apparent RMT Noise and Factors in Large Sample Correlation Matrices


  • Y. Malevergne

    (Univ. Nice and Univ. Lyon)

  • D. Sornette

    (CNRS-Univ. Nice and UCLA)


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.

Suggested Citation

  • Y. Malevergne & D. Sornette, 2002. "Collective Origin of the Coexistence of Apparent RMT Noise and Factors in Large Sample Correlation Matrices," Papers cond-mat/0210115,
  • Handle: RePEc:arx:papers:cond-mat/0210115

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    Cited by:

    1. Thomas Conlon & Heather J. Ruskin & Martin Crane, 2010. "Cross-Correlation Dynamics in Financial Time Series," Papers 1002.0321,
    2. Dalibor Eterovic & Nicolas Eterovic, 2012. "Separating the Wheat from the Chaff: Understanding Portfolio Returns in an Emerging Market," Working Papers wp_025, Adolfo Ibáñez University, School of Government.

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