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

Author

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  • Livan, Giacomo
  • Alfarano, Simone
  • Scalas, Enrico

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.

Suggested Citation

  • Livan, Giacomo & Alfarano, Simone & Scalas, Enrico, 2011. "The fine structure of spectral properties for random correlation matrices: an application to financial markets," MPRA Paper 28964, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:28964
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    1. repec:taf:quantf:v:17:y:2017:i:2:p:289-297 is not listed on IDEAS
    2. Giacomo Livan & Simone Alfarano & Mishael Milaković & Enrico Scalas, 2015. "A spectral perspective on excess volatility," Applied Economics Letters, Taylor & Francis Journals, vol. 22(9), pages 745-750, June.
    3. Matthias Raddant & Friedrich Wagner, 2016. "Phase transition in the S&P stock market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 11(2), pages 229-246, October.
    4. Longfeng Zhao & Wei Li & Andrea Fenu & Boris Podobnik & Yougui Wang & H. Eugene Stanley, 2017. "The q-dependent detrended cross-correlation analysis of stock market," Papers 1705.01406, arXiv.org, revised Jun 2017.
    5. Fricke, Daniel, 2012. "Trading strategies in the overnight money market: Correlations and clustering on the e-MID trading platform," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6528-6542.
    6. Matthias Raddant & Friedrich Wagner, 2017. "Transitions in the stock markets of the US, UK and Germany," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 289-297, February.
    7. Thomas Bury, 2014. "Collective behaviours in the stock market -- A maximum entropy approach," Papers 1403.5179, arXiv.org, revised Mar 2014.
    8. Thomas Bury, 2013. "Predicting trend reversals using market instantaneous state," Papers 1310.8169, arXiv.org, revised Mar 2014.
    9. Giacomo Livan & Luca Rebecchi, 2012. "Asymmetric correlation matrices: an analysis of financial data," Papers 1201.6535, arXiv.org, revised Apr 2012.
    10. Gerardo-Giorda, Luca & Germano, Guido & Scalas, Enrico, 2015. "Large scale simulation of synthetic markets," LSE Research Online Documents on Economics 67563, London School of Economics and Political Science, LSE Library.
    11. 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.
    12. Bury, Thomas, 2014. "Predicting trend reversals using market instantaneous state," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 79-91.
    13. 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.

    More about this item

    Keywords

    random matrix theroy; financial econometrics; correlation matrix;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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