Skip to main content
SpringerLink
Log in

Cross-correlations and structures of stock markets based on multiscale MF-DXA and PCA

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Based on the daily closing prices of US and Chinese stock markets, we conduct empirical analysis of the cross-correlations and multiscale distances among the US stock markets and China stock markets using the proposed multiscale multifractal detrended cross-correlation analysis method (MSMF-DXA). It is demonstrated that stock markets appear to be far more complex than hitherto reported in the studies using a fixed time scale. In order to identify and compare the interactions and structures of stock markets during financial crisis, as well as in the pre-crisis and post-crisis periods, all the entire samples are divided into four sub-periods. We are thus able to deeply examine the dynamics of linkages among stock markets during different considered periods by MSMF-DXA and principal component analysis technology. The empirical results indicate that both two financial crises cause the increase of international transmission of stock markets, but the global financial crisis and Asian financial crisis lead to different effects in stock markets. It is indicated that the markets are more correlated during global financial crisis compared to Asian financial crisis. The cross-correlations, especially for the markets within different geographic region, increased significantly during the crisis. It is shown that stock markets can be described by the first and second principal component during normal and crisis period, respectively. The results presented in this paper are useful to interpret the multiscale properties of stock markets and describe the dynamics of interactions among considered stock markets.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Ederington, L.H., Lee, J.H.: How markets process information:news releases and volatility. J. Financ. 48, 1161–1191 (1993)

    Article  Google Scholar 

  2. Balduzzi, P., Elton, E.J., Green, T.C.: Economic news and bond prices: evidence from the U.S. treasury market. J. Financ. Quant. Anal. 36, 523–543 (2001)

    Article  Google Scholar 

  3. Andersen, T.G., Bollerslev, T., Diebold, F.X., Vega, C.: Real-time price discovery in global stock, bond and foreign exchange markets. J. Int. Econ. 73, 251–277 (2007)

    Article  Google Scholar 

  4. Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Guhr, T., Stanley, H.E.: Random matrix approach to cross correlations in financial data. Phys. Rev. E 65, 066126 (2002)

    Article  Google Scholar 

  5. Podobnik, B., Horvatic, D., Petersen, A.M., Stanley, H.E.: Cross-correlations between volume change and price change. Proc. Natl. Acad. Sci. USA 106, 22079–22084 (2009)

    Article  MATH  Google Scholar 

  6. Zunino, L., Zanin, M., Tabak, B.M., Pérez, D.G., Rosso, O.A.: Complexity-entropy causality plane: a useful approach to quantify the stock market inefficiency. Phys. A 389, 1891–1901 (2010)

  7. Zhao, X.J., Shang, P.J., Pang, Y.L.: Power law and stretched exponential effects of extreme events in Chinese stock markets. Fluct. Noise Lett. 9, 203–217 (2010)

    Article  Google Scholar 

  8. Marschinski, R., Kantz, H.: Analyzing the information flow between financial time series. Eur. Phys. J. B 30, 275–281 (2002)

    Article  MathSciNet  Google Scholar 

  9. Utsugi, A., Ino, K., Oshikawa, M.: Random matrix theory analysis of cross correlations in financial markets. Phys. Rev. E 70, 026110 (2004)

    Article  Google Scholar 

  10. Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Stanley, H.E.: Universal and nonuniversal properties of cross correlations in financial time series. Phys. Rev. Lett. 83, 1471–1474 (1999)

    Article  Google Scholar 

  11. Shi, W.B., Shang, P.J., Wang, J., Lin, A.J.: Multiscale multifractal detrended cross-correlation analysis of financial time series. Phys. A 403, 35–44 (2014)

    Article  Google Scholar 

  12. Preis, T., Kenett, D.Y., Stanley, H.E., Helbing, D., Ben-Jacob, E.: Quantifying the behavior of stock correlations under market stress. Sci. Rep. 2, 752 (2012)

    Google Scholar 

  13. Shi, W.B., Shang, P.J.: Cross-sample entropy statistic as a measure of synchronism and and cross-correlation of stock markets. Nonlinear Dyn. 73, 539–554 (2013)

    Article  MathSciNet  Google Scholar 

  14. Kullmann, L., Kertesz, J., Kaski, K.: Time-dependent cross-correlations between different stock returns: a directed network of influence. Phys. Rev. E 66, 026125–026130 (2002)

    Article  Google Scholar 

  15. Rosenow, B., Gopikrishnan, P., Plerou, V., Stanley, H.E.: Dynamics of cross-correlations in the stock market. Phys. A 324, 241–246 (2003)

    Article  MATH  Google Scholar 

  16. Wilcox, D., Gebbie, T.: On the analysis of cross-correlations in South African market data. Phys. A 344, 294–298 (2004)

    Article  Google Scholar 

  17. Wilcox, D., Gebbie, T.: An analysis of cross-correlations in an emerging market. Phys. A 375, 584–598 (2007)

    Article  Google Scholar 

  18. Yu, C.H., Wu, C.C.: Economic sources of asymmetric cross-correlation among stock returns. Int. Rev. Econ. Financ. 10, 19–40 (2001)

    Article  Google Scholar 

  19. Forbes, K., Rigobon, R.: No contagion, only interdependence: measuring stock market comovements. J. Financ. 57, 2223–2261 (2002)

    Article  Google Scholar 

  20. Kenourgios, D., Samitas, A., Paltalidis, N.: Financial crisis and stock market contagion in multivariate time-varying asymmetric framework. J. Int. Financ. Markets 21, 92–106 (2011)

    Article  Google Scholar 

  21. Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E.: Mosaic organization of DNA sequences. Phy. Rev. E. 49, 1685–1689 (1994)

    Article  Google Scholar 

  22. Shang, P.J., Lu, Y.B., Kamae, S.: Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis. Chaos Solitons Fractals 36, 82–90 (2008)

    Article  Google Scholar 

  23. Shang, P.J., Lin, A.J., Liu, L.: Chaotic SVD method for minimizing the effect of exponential trends in detrended fluctuation analysis. Phys. A 388, 720–726 (2009)

    Article  Google Scholar 

  24. Kantelhardt, J.W., Zschiegner, S.A., Koscielny-Bunde, E., Havlin, S., Bunde, A., Stanley, H.E.: Multifractal detrended fluctuation analysis of nonstationary time series. Phys. A 316, 87–114 (2002)

    Article  MATH  Google Scholar 

  25. Costa, R., Vasconcelos, G.L.: Long-range correlations and nonstationarity in the Brazilian stock market. Phys. A 329, 231–248 (2003)

    Article  MATH  Google Scholar 

  26. Greene, M.T., Fieltz, B.D.: Long term dependence in common stock returns. J Financ. Econ. 4, 249–339 (1997)

    Google Scholar 

  27. Podobnik, B., Horvatic, D., Lam, A.N., Stanley, H.E., Ivanov, P.C.: Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes. Phys. A 387, 3954–3959 (2008)

    Article  MathSciNet  Google Scholar 

  28. Podobnik, B., Grosse, I., Horvatić, D., Ilic, S., Ivanov, P.C., Stanley, H.E.: Quantifying cross-correlations using local and global detrending approaches. Eur. Phys. J. B 71, 243–250 (2009)

    Article  Google Scholar 

  29. Podobnik, B., Stanley, H.E.: Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. Phy. Rev. Lett. 100, 084102 (2008)

    Article  Google Scholar 

  30. Zhou, W.X.: Multifractal detrended cross-correlation analysis for two nonstationary signals. Phys. Rev. E 77, 066211 (2008)

    Article  Google Scholar 

  31. Hajian, S., Movahed, M.S.: Multifractal detrended cross-correlation analysis of sunspot numbers and river flow fluctuations. Phys. A 389, 4942–4957 (2010)

    Article  Google Scholar 

  32. Cao, G.X., Xu, L.B., Gao, J.: Multifractal detrended cross-correlations between the Chinese exchange market and stock market. Phys. A 391, 4855–4866 (2012)

    Article  Google Scholar 

  33. Lin, A.J., Shang, P.J., Zhao, X.J.: The cross-correlations of stock markets based on DCCA and time-delay DCCA. Nonlinear Dyn. 67, 425–435 (2012)

    Article  MathSciNet  Google Scholar 

  34. Castiglioni, P., Parati, G., Lombardi, C., Quintin, L., Di Rienzo, M.: Assessing the fractal structure of heart rate by the temporal spectrum of scale exponents: a new approach for detrended fluctuation analysis of heart rate variability. Biomed. Tech. 56, 175–183 (2010)

  35. Gierałtowski, J., Żebrowski, J.J., Baranowski, R.: Multiscale multifractal analysis of heart rate variability recordings with a large number of occurrences of arrhythmia. Phys. Rev. E 85, 021915 (2012)

  36. Lu, G.D., Zhang, C.M., Zhang, T.Y., Zhang, W.: Kernel based symmetrical principal component analysis for face classification. Neurocomput 70, 904–911 (2007)

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 61304145, 61071142, and 61371130), the China Postdoctoral Science Foundation (Grant No. 2012M520156), the Fundamental Research Funds for the Central Universities (Grant No. 2013JBM089), the Research Fund for the Doctoral Program of Higher Education (Grant No. 20130009120016), and the National High Technology Research Development Program of China (Grant No. 2011AA110306).

Author information

Authors and Affiliations

  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Aijing Lin & Pengjian Shang

  2. School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Huachun Zhou

Authors
  1. Aijing Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pengjian Shang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huachun Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aijing Lin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, A., Shang, P. & Zhou, H. Cross-correlations and structures of stock markets based on multiscale MF-DXA and PCA. Nonlinear Dyn 78, 485–494 (2014). https://doi.org/10.1007/s11071-014-1455-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1455-5

Keywords

Search

Navigation