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Collective origin of the coexistence of apparent random matrix theory noise and of factors in large sample correlation matrices

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  • Malevergne, Y.
  • Sornette, D.

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.

Suggested Citation

  • Malevergne, Y. & Sornette, D., 2004. "Collective origin of the coexistence of apparent random matrix theory noise and of factors in large sample correlation matrices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 660-668.
    • Handle: RePEc:eee:phsmap:v:331:y:2004:i:3:p:660-668
    DOI: 10.1016/j.physa.2003.09.004
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    Cited by:

    1. Eterovic, Nicolas A. & Eterovic, Dalibor S., 2013. "Separating the wheat from the chaff: Understanding portfolio returns in an emerging market," Emerging Markets Review, Elsevier, vol. 16(C), pages 145-169.
    2. Martins, André C.R., 2007. "Non-stationary correlation matrices and noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 552-558.
    3. Conlon, T. & Ruskin, H.J. & Crane, M., 2009. "Cross-correlation dynamics in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 705-714.
    4. Bommarito, Michael J. & Duran, Ahmet, 2018. "Spectral analysis of time-dependent market-adjusted return correlation matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 273-282.
    5. Ñíguez, Trino-Manuel & Perote, Javier, 2016. "Multivariate moments expansion density: Application of the dynamic equicorrelation model," Journal of Banking & Finance, Elsevier, vol. 72(S), pages 216-232.
    6. Stephan Süss, 2012. "The pricing of idiosyncratic risk: evidence from the implied volatility distribution," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(2), pages 247-267, June.
    7. Wang, Gang-Jin & Xie, Chi & Chen, Shou & Yang, Jiao-Jiao & Yang, Ming-Yan, 2013. "Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3715-3730.
    8. Antti J. Tanskanen & Jani Lukkarinen & Kari Vatanen, 2016. "Random selection of factors preserves the correlation structure in a linear factor model to a high degree," Papers 1604.05896, arXiv.org, revised Dec 2018.
    9. Antti J Tanskanen & Jani Lukkarinen & Kari Vatanen, 2018. "Random selection of factors preserves the correlation structure in a linear factor model to a high degree," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-22, December.
    10. 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.
    11. Anshul Verma & Riccardo Junior Buonocore & Tiziana di Matteo, 2017. "A cluster driven log-volatility factor model: a deepening on the source of the volatility clustering," Papers 1712.02138, arXiv.org, revised May 2018.

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