IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v11y2011i7p1103-1124.html
   My bibliography  Save this article

Applying free random variables to random matrix analysis of financial data. Part I: The Gaussian case

Author

Listed:
  • Zdzisław Burda
  • Andrzej Jarosz
  • Maciej Nowak
  • Jerzy Jurkiewicz
  • Gabor Papp
  • Ismail Zahed

Abstract

We apply the concept of free random variables to doubly correlated (Gaussian) Wishart random matrix models, appearing, for example, in a multivariate analysis of financial time series, and displaying both inter-asset cross-covariances and temporal auto-covariances. We give a comprehensive introduction to the rich financial reality behind such models. We explain in an elementary way the main techniques of free random variables calculus, with a view to promoting them in the quantitative finance community. We apply our findings to tackle several financially relevant problems, such as a universe of assets displaying exponentially decaying temporal covariances, or the exponentially weighted moving average, both with an arbitrary structure of cross-covariances.

Suggested Citation

  • Zdzisław Burda & Andrzej Jarosz & Maciej Nowak & Jerzy Jurkiewicz & Gabor Papp & Ismail Zahed, 2011. "Applying free random variables to random matrix analysis of financial data. Part I: The Gaussian case," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1103-1124.
    • Handle: RePEc:taf:quantf:v:11:y:2011:i:7:p:1103-1124
    DOI: 10.1080/14697688.2010.484025
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697688.2010.484025
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2010.484025?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. K. B. K. Mayya & R. E. Amritkar, 2006. "Analysis of delay correlation matrices," Papers cond-mat/0601279, arXiv.org.
    2. Christoly Biely & Stefan Thurner, 2008. "Random matrix ensembles of time-lagged correlation matrices: derivation of eigenvalue spectra and analysis of financial time-series," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 705-722.
    3. Szilard Pafka & Marc Potters & Imre Kondor, 2004. "Exponential Weighting and Random-Matrix-Theory-Based Filtering of Financial Covariance Matrices for Portfolio Optimization," Papers cond-mat/0402573, arXiv.org.
    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. Desislava Chetalova & Rudi Schafer & Thomas Guhr, 2014. "Zooming into market states," Papers 1406.5386, arXiv.org.
    2. Vincent Tan & Stefan Zohren, 2020. "Estimation of Large Financial Covariances: A Cross-Validation Approach," Papers 2012.05757, arXiv.org, revised Jan 2023.
    3. Collins, Benoît & Matsumoto, Sho & Saad, Nadia, 2014. "Integration of invariant matrices and moments of inverses of Ginibre and Wishart matrices," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 1-13.
    4. 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.
    5. 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.
    6. Michael C Münnix & Rudi Schäfer & Thomas Guhr, 2014. "A Random Matrix Approach to Credit Risk," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-9, May.

    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. Sebastiano Michele Zema & Giorgio Fagiolo & Tiziano Squartini & Diego Garlaschelli, 2021. "Mesoscopic Structure of the Stock Market and Portfolio Optimization," Papers 2112.06544, arXiv.org.
    2. Vincent Tan & Stefan Zohren, 2020. "Estimation of Large Financial Covariances: A Cross-Validation Approach," Papers 2012.05757, arXiv.org, revised Jan 2023.
    3. Stefanos Bennett & Mihai Cucuringu & Gesine Reinert, 2022. "Lead-lag detection and network clustering for multivariate time series with an application to the US equity market," Papers 2201.08283, arXiv.org.
    4. Mahsa Ghorbani & Edwin K P Chong, 2020. "Stock price prediction using principal components," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-20, March.
    5. Sandoval, Leonidas Junior, 2013. "To lag or not to lag? How to compare indices of stock markets that operate at different times," Insper Working Papers wpe_319, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    6. Gilles Zumbach, 2011. "Empirical properties of large covariance matrices," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1091-1102.
    7. Brian Opiyo Yalla & Ferdinand Okoth Othieno, 2023. "Modelling delayed correlation between interest rates and equity market returns," SN Business & Economics, Springer, vol. 3(2), pages 1-24, February.
    8. Svensson, Jens, 2007. "The asymptotic spectrum of the EWMA covariance estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 621-630.
    9. Mahsa Ghorbani & Edwin K. P. Chong, 2022. "A dimension reduction method for stock-price prediction using multiple predictors," Operational Research, Springer, vol. 22(3), pages 2859-2878, July.
    10. Hirschberger, Markus & Qi, Yue & Steuer, Ralph E., 2007. "Randomly generating portfolio-selection covariance matrices with specified distributional characteristics," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1610-1625, March.
    11. 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.
    12. Hongli Zeng & R'emi Lemoy & Mikko Alava, 2013. "Financial interaction networks inferred from traded volumes," Papers 1311.3871, arXiv.org.
    13. Ochiai, Tomoshiro & Nacher, Jose C., 2022. "Unveiling the directional network behind financial statements data using volatility constraint correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    14. S. Valeyre & D. S. Grebenkov & S. Aboura, 2018. "Emergence of correlations between securities at short time scales," Papers 1807.05015, arXiv.org.
    15. Sebastien Valeyre & Denis S Grebenkov & Sofiane Aboura, 2019. "Emergence of correlations between securities at short time scales," Post-Print hal-02343888, HAL.
    16. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.
    17. Cai, Yumei & Cui, Xiaomei & Huang, Qianyun & Sun, Jianqiang, 2017. "Hierarchy, cluster, and time-stable information structure of correlations between international financial markets," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 562-573.
    18. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
    19. Alejandro Rodriguez Dominguez, 2022. "Portfolio Optimization based on Neural Networks Sensitivities from Assets Dynamics respect Common Drivers," Papers 2202.08921, arXiv.org, revised Dec 2022.

    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:taf:quantf:v:11:y:2011:i:7:p:1103-1124. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.