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The fine structure of spectral properties for random correlation matrices: an application to financial markets

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  • G. Livan
  • S. Alfarano
  • E. Scalas

Abstract

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross-correlations between stocks. We interpret and corroborate these findings in terms of factor models, and and we compare empirical spectra to those predicted by Random Matrix Theory for such models.

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File URL: http://arxiv.org/pdf/1102.4076
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Paper provided by arXiv.org in its series Papers with number 1102.4076.

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Date of creation: Feb 2011
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Publication status: Published in Phys. Rev. E 84, 016113 (2011)
Handle: RePEc:arx:papers:1102.4076

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Cited by:
  1. Daniel Fricke, 2012. "Trading Strategies in the Overnight Money Market: Correlations and Clustering on the e-MID Trading Platform," Kiel Working Papers 1766, Kiel Institute for the World Economy.
  2. Thomas Bury, 2013. "Predicting trend reversals using market instantaneous state," Papers 1310.8169, arXiv.org, revised Mar 2014.
  3. Matthias Raddant & Friedrich Wagner, 2013. "Phase Transition in the S&P Stock Market," Papers 1306.2508, arXiv.org.
  4. Thomas Bury, 2014. "Collective behaviours in the stock market -- A maximum entropy approach," Papers 1403.5179, arXiv.org, revised Mar 2014.
  5. Giacomo Livan & Jun-ichi Inoue & Enrico Scalas, 2012. "On the non-stationarity of financial time series: impact on optimal portfolio selection," Papers 1205.0877, arXiv.org, revised Jul 2012.

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