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The cross-correlation analysis of multi property of stock markets based on MM-DFA

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  • Yang, Yujun
  • Li, Jianping
  • Yang, Yimei

Abstract

In this paper, we propose a new method called DH-MXA based on distribution histograms of Hurst surface and multiscale multifractal detrended fluctuation analysis. The method allows us to investigate the cross-correlation characteristics among multiple properties of different stock time series. It may provide a new way of measuring the nonlinearity of several signals. It also can provide a more stable and faithful description of cross-correlation of multiple properties of stocks. The DH-MXA helps us to present much richer information than multifractal detrented cross-correlation analysis and allows us to assess many universal and subtle cross-correlation characteristics of stock markets. We show DH-MXA by selecting four artificial data sets and five properties of four stock time series from different countries. The results show that our proposed method can be adapted to investigate the cross-correlation of stock markets. In general, the American stock markets are more mature and less volatile than the Chinese stock markets.

Suggested Citation

  • Yang, Yujun & Li, Jianping & Yang, Yimei, 2017. "The cross-correlation analysis of multi property of stock markets based on MM-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 23-33.
    • Handle: RePEc:eee:phsmap:v:481:y:2017:i:c:p:23-33
    DOI: 10.1016/j.physa.2017.04.005
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    as
    1. Bacry, E. & Delour, J. & Muzy, J.F., 2001. "Modelling financial time series using multifractal random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 84-92.
    2. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
    3. Yu, Chih-Hsien & Wu, Chunchi, 2001. "Economic sources of asymmetric cross-correlation among stock returns," International Review of Economics & Finance, Elsevier, vol. 10(1), pages 19-40.
    4. Pan, Raj Kumar & Sinha, Sitabhra, 2008. "Inverse-cubic law of index fluctuation distribution in Indian markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2055-2065.
    5. Yanhui Liu & Parameswaran Gopikrishnan & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1999. "The statistical properties of the volatility of price fluctuations," Papers cond-mat/9903369, arXiv.org, revised Mar 1999.
    6. Kim, Kyungsik & Yoon, Seong-Min, 2004. "Multifractal features of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 272-278.
    7. Shang, Pengjian & Lin, Aijing & Liu, Liang, 2009. "Chaotic SVD method for minimizing the effect of exponential trends in detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 720-726.
    8. Gopikrishnan, P & Plerou, V & Liu, Y & Amaral, L.A.N & Gabaix, X & Stanley, H.E, 2000. "Scaling and correlation in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 362-373.
    9. Greene, Myron T. & Fielitz, Bruce D., 1977. "Long-term dependence in common stock returns," Journal of Financial Economics, Elsevier, vol. 4(3), pages 339-349, May.
    10. Zhi-Qiang Jiang & Wei-Xing Zhou, 2011. "Multifractal detrending moving average cross-correlation analysis," Papers 1103.2577, arXiv.org, revised Mar 2011.
    11. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    12. B. Podobnik & D. F. Fu & H. E. Stanley & P. Ch. Ivanov, 2007. "Power-law autocorrelated stochastic processes with long-range cross-correlations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(1), pages 47-52, March.
    13. Shi, Wenbin & Shang, Pengjian & Wang, Jing & Lin, Aijing, 2014. "Multiscale multifractal detrended cross-correlation analysis of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 35-44.
    14. Balduzzi, Pierluigi & Elton, Edwin J. & Green, T. Clifton, 2001. "Economic News and Bond Prices: Evidence from the U.S. Treasury Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 36(4), pages 523-543, December.
    15. Wilcox, Diane & Gebbie, Tim, 2007. "An analysis of cross-correlations in an emerging market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 584-598.
    16. B. Podobnik & I. Grosse & D. Horvatić & S. Ilic & P. Ch. Ivanov & H. E. Stanley, 2009. "Quantifying cross-correlations using local and global detrending approaches," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(2), pages 243-250, September.
    17. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Vega, Clara, 2007. "Real-time price discovery in global stock, bond and foreign exchange markets," Journal of International Economics, Elsevier, vol. 73(2), pages 251-277, November.
    18. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    19. Pierre Cizeau & Yanhui Liu & Martin Meyer & C. -K. Peng & H. Eugene Stanley, 1997. "Volatility distribution in the S&P500 Stock Index," Papers cond-mat/9708143, arXiv.org.
    20. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
    21. Oh, Gabjin & Kim, Ho-yong & Ahn, Seok-Won & Kwak, Wooseop, 2015. "Analyzing the financial crisis using the entropy density function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 464-469.
    22. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2010. "Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1891-1901.
    23. Lin, Aijing & Ma, Hui & Shang, Pengjian, 2015. "The scaling properties of stock markets based on modified multiscale multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 525-537.
    24. Cizeau, Pierre & Liu, Yanhui & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Volatility distribution in the S&P500 stock index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 441-445.
    25. Zebende, G.F., 2011. "DCCA cross-correlation coefficient: Quantifying level of cross-correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 614-618.
    26. Costa, Rogério L. & Vasconcelos, G.L., 2003. "Long-range correlations and nonstationarity in the Brazilian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 231-248.
    27. Podobnik, Boris & Horvatic, Davor & Lam Ng, Alfonso & Eugene Stanley, H. & Ivanov, Plamen Ch., 2008. "Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3954-3959.
    28. R. L. Costa & G. L. Vasconcelos, 2003. "Long-range correlations and nonstationarity in the Brazilian stock market," Papers cond-mat/0302342, arXiv.org.
    29. Hasan, Rashid & Mohammad, Salim M., 2015. "Multifractal analysis of Asian markets during 2007–2008 financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 746-761.
    30. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    31. Hajian, S. & Movahed, M. Sadegh, 2010. "Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4942-4957.
    32. Rosenow, Bernd & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Eugene Stanley, H, 2003. "Dynamics of cross-correlations in the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 241-246.
    33. L. Kullmann & J. Kertesz & K. Kaski, 2002. "Time dependent cross correlations between different stock returns: A directed network of influence," Papers cond-mat/0203256, arXiv.org, revised May 2002.
    34. Wilcox, Diane & Gebbie, Tim, 2004. "On the analysis of cross-correlations in South African market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 294-298.
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