IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1102.4076.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.

Suggested Citation

  • G. Livan & S. Alfarano & E. Scalas, 2011. "The fine structure of spectral properties for random correlation matrices: an application to financial markets," Papers 1102.4076, arXiv.org.
    • Handle: RePEc:arx:papers:1102.4076
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1102.4076
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. M. Raddant & T. Di Matteo, 2023. "A look at financial dependencies by means of econophysics and financial economics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(4), pages 701-734, October.
    3. 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.
    4. 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.
    5. 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.
    6. Thomas Bury, 2013. "Predicting trend reversals using market instantaneous state," Papers 1310.8169, arXiv.org, revised Mar 2014.
    7. Giacomo Livan & Luca Rebecchi, 2012. "Asymmetric correlation matrices: an analysis of financial data," Papers 1201.6535, arXiv.org, revised Apr 2012.
    8. Raddant, Matthias & Wagner, Friedrich, 2013. "Phase transition in the S&P stock market," Kiel Working Papers 1846, Kiel Institute for the World Economy (IfW Kiel).
    9. 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.
    10. Yi†Hui Zhou & J. S. Marron & Fred A. Wright, 2018. "Eigenvalue significance testing for genetic association," Biometrics, The International Biometric Society, vol. 74(2), pages 439-447, June.
    11. Thomas Bury, 2014. "Collective behaviours in the stock market -- A maximum entropy approach," Papers 1403.5179, arXiv.org, revised Mar 2014.
    12. 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.
    13. Riccardo Marcaccioli & Giacomo Livan, 2019. "Maximum Entropy approach to multivariate time series randomization," Papers 1907.04925, arXiv.org, revised Jun 2020.
    14. Marcaccioli, Riccardo & Livan, Giacomo, 2020. "Maximum entropy approach to multivariate time series randomization," LSE Research Online Documents on Economics 115284, London School of Economics and Political Science, LSE Library.
    15. Bury, Thomas, 2014. "Predicting trend reversals using market instantaneous state," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 79-91.
    16. 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.
    17. Anshul Verma & Orazio Angelini & Tiziana Di Matteo, 2019. "A new set of cluster driven composite development indicators," Papers 1911.11226, arXiv.org, revised Mar 2020.
    18. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fabrizio Pomponio & Frédéric Abergel, 2013. "Multiple-limit trades : empirical facts and application to lead-lag measures," Post-Print hal-00745317, HAL.
    2. Lubashevsky, Ihor & Friedrich, Rudolf & Heuer, Andreas & Ushakov, Andrey, 2009. "Generalized superstatistics of nonequilibrium Markovian systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4535-4550.
    3. Assaf Almog & Ferry Besamusca & Mel MacMahon & Diego Garlaschelli, 2015. "Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-16, July.
    4. Sebastiano Michele Zema & Giorgio Fagiolo & Tiziano Squartini & Diego Garlaschelli, 2021. "Mesoscopic Structure of the Stock Market and Portfolio Optimization," Papers 2112.06544, arXiv.org.
    5. S. Reimann, 2007. "Price dynamics from a simple multiplicative random process model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(4), pages 381-394, April.
    6. Dror Y. Kenett & Xuqing Huang & Irena Vodenska & Shlomo Havlin & H. Eugene Stanley, 2015. "Partial correlation analysis: applications for financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 15(4), pages 569-578, April.
    7. W.-S. Jung & F. Z. Wang & S. Havlin & T. Kaizoji & H.-T. Moon & H. E. Stanley, 2008. "Volatility return intervals analysis of the Japanese market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(1), pages 113-119, March.
    8. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    9. Xiao, Di & Wang, Jun, 2021. "Attitude interaction for financial price behaviours by contact system with small-world network topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    10. Paulo Ferreira & Éder J.A.L. Pereira & Hernane B.B. Pereira, 2020. "From Big Data to Econophysics and Its Use to Explain Complex Phenomena," JRFM, MDPI, vol. 13(7), pages 1-10, July.
    11. V. Alfi & L. Pietronero & A. Zaccaria, 2008. "Minimal Agent Based Model For The Origin And Self-Organization Of Stylized Facts In Financial Markets," Papers 0807.1888, arXiv.org.
    12. Denis Phan, 2006. "Discrete Choices under Social Influence:Generic Properties," Post-Print halshs-00105857, HAL.
    13. Slanina, František, 2010. "A contribution to the systematics of stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3230-3239.
    14. Dibeh, Ghassan, 2007. "Contagion effects in a chartist–fundamentalist model with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 52-57.
    15. Guégan, Dominique & Ielpo, Florian & Lalaharison, Hanjarivo, 2013. "Option pricing with discrete time jump processes," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2417-2445.
    16. Till Massing, 2018. "Simulation of Student–Lévy processes using series representations," Computational Statistics, Springer, vol. 33(4), pages 1649-1685, December.
    17. Guevara Hidalgo, Esteban, 2017. "Bin size independence in intra-day seasonalities for relative prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 722-732.
    18. F. Wang & P. Weber & K. Yamasaki & S. Havlin & H. E. Stanley, 2007. "Statistical regularities in the return intervals of volatility," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 123-133, January.
    19. Anufriev, Mikhail & Bottazzi, Giulio & Marsili, Matteo & Pin, Paolo, 2012. "Excess covariance and dynamic instability in a multi-asset model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1142-1161.
    20. X. F. Jiang & T. T. Chen & B. Zheng, 2013. "Time-reversal asymmetry in financial systems," Papers 1308.0669, arXiv.org.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1102.4076. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.