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Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

Author

Listed:
  • Wang, Gang-Jin
  • Xie, Chi
  • Chen, Shou
  • Yang, Jiao-Jiao
  • Yang, Ming-Yan

Abstract

In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Marčenko–Pastur distribution.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:17:p:3715-3730
    DOI: 10.1016/j.physa.2013.04.027
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    2. 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.
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    6. Huang, Xuan & An, Haizhong & Fang, Wei & Gao, Xiangyun & Wang, Lijun & Sun, Xiaoqi, 2016. "Impact assessment of international anti-dumping events on synchronization and comovement of the Chinese photovoltaic stocks," Renewable and Sustainable Energy Reviews, Elsevier, vol. 59(C), pages 459-469.
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    9. Liu, Li, 2014. "Cross-correlations between crude oil and agricultural commodity markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 293-302.
    10. 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.
    11. 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.
    12. Wang, Gang-Jin & Xie, Chi & He, Ling-Yun & Chen, Shou, 2014. "Detrended minimum-variance hedge ratio: A new method for hedge ratio at different time scales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 70-79.
    13. Guedes, E. & Dionísio, A. & Ferreira, P.J. & Zebende, G.F., 2017. "DCCA cross-correlation in blue-chips companies: A view of the 2008 financial crisis in the Eurozone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 38-47.
    14. Kalyagin, V.A. & Koldanov, A.P. & Koldanov, P.A. & Pardalos, P.M. & Zamaraev, V.A., 2014. "Measures of uncertainty in market network analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 59-70.
    15. 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.
    16. repec:kap:compec:v:51:y:2018:i:3:d:10.1007_s10614-016-9627-7 is not listed on IDEAS
    17. Jan Jurczyk & Alexander Eckrot, 2015. "Cross correlations in European government bonds and EuroStoxx," Papers 1502.07367, arXiv.org, revised Jul 2015.

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