IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v567y2021ics0378437120310116.html
   My bibliography  Save this article

Analyzing financial correlation matrix based on the eigenvector–eigenvalue identity

Author

Listed:
  • Nie, Chun-Xiao

Abstract

Previous empirical studies have shown that correlation matrices in financial markets usually have dominant eigenvalues. This paper applies a classic eigenvector–eigenvalue identity to analyze the properties of financial correlation matrices with super-dominant eigenvalues. Empirical analysis shows that there is an approximate relationship between the maximum eigenvalue and the eigenvector component. If the correlation matrix has a super eigenvalue, we can estimate the maximum eigenvalue of the sub-matrix from the maximum eigenvalue of the large-dimensional correlation matrix. Conversely, we can also estimate the maximum eigenvalue of the correlation matrix of a large number of stocks from the maximum eigenvalues corresponding to a few stocks. In addition, we find that different stock sets constructed based on the components of the eigenvector generate different predicted values, and the most accurate estimates can be obtained by selecting stocks at equal intervals. This paper reveals that eigenvector–eigenvalue identity helps to analyze the spectrum of financial correlation matrix in depth.

Suggested Citation

  • Nie, Chun-Xiao, 2021. "Analyzing financial correlation matrix based on the eigenvector–eigenvalue identity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    • Handle: RePEc:eee:phsmap:v:567:y:2021:i:c:s0378437120310116
    DOI: 10.1016/j.physa.2020.125713
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120310116
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2020.125713?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. Ajay Singh & Dinghai Xu, 2016. "Random matrix application to correlations amongst the volatility of assets," Quantitative Finance, Taylor & Francis Journals, vol. 16(1), pages 69-83, January.
    2. Sharifi, S. & Crane, M. & Shamaie, A. & Ruskin, H., 2004. "Random matrix theory for portfolio optimization: a stability approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 629-643.
    3. Conlon, T. & Ruskin, H.J. & Crane, M., 2007. "Random matrix theory and fund of funds portfolio optimisation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 565-576.
    4. Joël Bun & Jean-Philippe Bouchaud & Marc Potters, 2017. "Cleaning large correlation matrices: tools from random matrix theory," Post-Print hal-01491304, HAL.
    5. Jiang, J. & Ma, K. & Cai, X., 2007. "Scaling and correlations in foreign exchange market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 274-280.
    6. Sunil Kumar & Nivedita Deo, 2012. "Correlation, Network and Multifractal Analysis of Global Financial Indices," Papers 1202.0409, arXiv.org.
    7. Vasiliki Plerou & Parameswaran Gopikrishnan & Bernd Rosenow & Luis A. Nunes Amaral & H. Eugene Stanley, 1999. "Universal and non-universal properties of cross-correlations in financial time series," Papers cond-mat/9902283, arXiv.org.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Conlon, T. & Ruskin, H.J. & Crane, M., 2009. "Cross-correlation dynamics in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 705-714.
    3. Wang, Gang-Jin & Xie, Chi, 2015. "Correlation structure and dynamics of international real estate securities markets: A network perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 176-193.
    4. Jovanovic, Franck & Mantegna, Rosario N. & Schinckus, Christophe, 2019. "When financial economics influences physics: The role of Econophysics," International Review of Financial Analysis, Elsevier, vol. 65(C).
    5. Chun-Xiao Nie, 2021. "Studying the correlation structure based on market geometry," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(2), pages 411-441, April.
    6. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.
    7. 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.
    8. 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.
    9. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2018. "Collective behavior of cryptocurrency price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 499-509.
    10. Conlon, T. & Ruskin, H.J. & Crane, M., 2007. "Random matrix theory and fund of funds portfolio optimisation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 565-576.
    11. Duc Thi Luu, 2022. "Portfolio Correlations in the Bank-Firm Credit Market of Japan," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 529-569, August.
    12. Gloria Polinesi & Maria Cristina Recchioni, 2021. "Filtered clustering for exchange traded fund," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 75(1), pages 125-135, January-M.
    13. Xinyu Wang & Liang Zhao & Ning Zhang & Liu Feng & Haibo Lin, 2022. "Stability of China's Stock Market: Measure and Forecast by Ricci Curvature on Network," Papers 2204.06692, arXiv.org.
    14. Chun-Xiao Nie & Fu-Tie Song, 2021. "Entropy of Graphs in Financial Markets," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1149-1166, April.
    15. Gao, Hai-Ling & Mei, Dong-Cheng, 2019. "The correlation structure in the international stock markets during global financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    16. Leonidas Sandoval Junior & Adriana Bruscato & Maria Kelly Venezuela, 2012. "Building portfolios of stocks in the S\~ao Paulo Stock Exchange using Random Matrix Theory," Papers 1201.0625, arXiv.org, revised Mar 2013.
    17. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa & Stosic, Tatijana, 2016. "Correlations of multiscale entropy in the FX market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 52-61.
    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.
    19. El Alaoui, Marwane, 2015. "Random matrix theory and portfolio optimization in Moroccan stock exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 92-99.
    20. Ankit Dangi, 2013. "Financial Portfolio Optimization: Computationally guided agents to investigate, analyse and invest!?," Papers 1301.4194, arXiv.org.

    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:eee:phsmap:v:567:y:2021:i:c:s0378437120310116. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.