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The bulk of the stock market correlation matrix is not pure noise

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  • Kwapień, J.
  • Drożdż, S.
  • Oświe¸cimka, P.

Abstract

We analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes. We use 100 highly capitalized stocks from the American market and relate the result to the corresponding ensemble of Wishart random matrices. It turns out that systematically more eigenvalues remain beyond the borders prescribed by this variant of the random matrix theory (RMT). This may indicate that even the bulk of the spectrum of the stock market correlation matrix carries some sort of correlations that are masked by a measurement noise when the time series used to construct the matrix are short. We also study some other characteristics of the “noisy” eigensignals, like their return distributions, temporal correlations or their multifractal spectra, and the results support the above conclusions.

Suggested Citation

  • Kwapień, J. & Drożdż, S. & Oświe¸cimka, P., 2006. "The bulk of the stock market correlation matrix is not pure noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 589-606.
    • Handle: RePEc:eee:phsmap:v:359:y:2006:i:c:p:589-606
    DOI: 10.1016/j.physa.2005.05.090
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    References listed on IDEAS

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    1. Thomas Lux, 2003. "The Multi-Fractal Model of Asset Returns:Its Estimation via GMM and Its Use for Volatility Forecasting," Computing in Economics and Finance 2003 14, Society for Computational Economics.
    2. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1997. "Large Deviations and the Distribution of Price Changes," Cowles Foundation Discussion Papers 1165, Cowles Foundation for Research in Economics, Yale University.
    3. Lux, Thomas, 2003. "Detecting multi-fractal properties in asset returns: The failure of the scaling estimator," Economics Working Papers 2003-14, Christian-Albrechts-University of Kiel, Department of Economics.
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    Citations

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    Cited by:

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    6. 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.
    7. Heckens, Anton J. & Guhr, Thomas, 2022. "New collectivity measures for financial covariances and correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    8. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    9. Thomas Guhr & Andreas Schell, 2020. "Exact Multivariate Amplitude Distributions for Non-Stationary Gaussian or Algebraic Fluctuations of Covariances or Correlations," Papers 2011.07570, arXiv.org.
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    11. Jan Jurczyk & Alexander Eckrot, 2015. "Cross correlations in European government bonds and EuroStoxx," Papers 1502.07367, arXiv.org, revised Jul 2015.

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