Abstract
In this paper, we employ cross-sample entropy (cross-SampEn), transfer entropy, and detrended cross-correlation analysis (DCCA) measurement to investigate the relationship between time series among different stock markets. Cross-SampEn method is used to compare the returns of every two stock index time series to assess their degree of asynchrony. Transfer entropy is applied to measure the information flow between two financial time series and this model-free approach in principle allows us to detect statistical dependencies of all types. We use DCCA method to quantify the cross-correlations of two non-stationary time series. We report the results of synchronism and cross-correlation behaviors in US and Chinese stock markets in periods 1991–1998 (before the Asian currency crisis) and 1999–2008 (after the Asian currency crises) by using cross-SampEn, transfer entropy and DCCA methods, respectively. The results, through the contrast description of the three methods, show that the synchronism and cross-correlation become higher after the Asian currency crises, especially for the three Chinese stock index time series. Among all these consequences, ShangZheng and ShenCheng show the strongest synchronism, information transfer and cross-correlation. While the three US stock markets show a good cross-correlation and information transfer, but less synchronism before the Asian currency crisis.
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References
Mantegna, R.N., Stanley, H.E.: Scaling behaviour in the dynamics of an economic index. Nature 376, 46–49 (1995)
Mantegna, R.N., Stanley, H.E.: An Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge (1999)
Laloux, L., Cizeau, P., Bouchaud, J.P., Potters, M.: Noise dressing of financial correlation matrices. Phys. Rev. Lett. 83, 1467–1470 (1999)
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)
Ma, W.J., Hu, C.K., Amritkar, R.E.: Stochastic dynamical model for stock-stock correlations. Phys. Rev. E 70, 026101 (2004)
Arthur, W.B., Durlauf, S.N., Lane, D.A.: The Economy as an Evolving Complex System II. Perseus Books, Cambridge (1997)
Mantegna, R.N., Stanley, H.E.: An Introduction to Econophysics. Cambridge University Press, Cambridge (2000)
Bouchaud, J.P., Potters, M.: Theory of Financial Risks. Cambridge University Press, Cambridge (2000)
Mandelbrot, B.B.: Scaling in financial prices: II. Multifractals and the star equation. Quant. Finance 1, 124 (2001)
Kullmann, L., Kert´esz, J., Mantegna, R.N.: Identification of clusters of companies in stock indices via Potts super-paramagnetic transitions. Physica A 287, 412 (2000)
Giada, L., Marsili, M.: Algorithms of maximum likelihood data clustering with applications. Physica A 315, 650 (2002)
Marschinski, R., Kantz, H.: Analysing the information flow between financial time series. An improved estimator for transfer entropy. Eur. Phys. J. B 30, 275–281 (2002)
Liu, L.Z., Qian, X.Y., Lu, H.Y.: Cross-Sample entropy of foreign exchange time series. Physica A 389, 4785–4792 (2010)
Pincus, S., Singer, B.: Randomness and degrees of irregularity. Proc. Natl. Acad. Sci. USA 93, 2083–2088 (1995)
Pincus, S.M., Mulligan, T., Iranmanesh, A., Gheorghiu, S., Godschalk, M., Veldhuis, J.D.: Older males secrete luteinizing hormone and testosterone more irregularly and jointly more asynchronously than younger males. Proc. Natl. Acad. Sci. USA 93, 14100–14105 (1996)
Richman, J.S., Moorman, J.R.: Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol., Heart Circ. Physiol. 278, 2039–2049 (2000)
Schreiber, T.: Measuring information transfer. Phys. Rev. Lett. 85, 461–464 (2000)
Marschinski, R., Kantz, H.: Analysing the information flow between financial time series, an improved estimator for transfer entropy. Eur. Phys. J. B 30, 275–281 (2002)
Kwon, O., Yang, J.S.: Information flow between composite stock index and individual stocks. Physica A 387, 2851–2856 (2008)
Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., Goldberger, A.L.: Mosaic organization of DNA sequences. Phys. Rev. E 49, 1685–1689 (1994)
Podobnik, B., Stanley, H.E.: Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. Phys. Rev. Lett. 100, 084102 (2008)
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)
Lake, D.E., Richman, J.S., Griffin, M.P., Moorman, J.R.: Sample entropy analysis of neonatal heart rate variability. Am. J. Physiol., Regul. Integr. Comp. Physiol. 283, 789–797 (2002)
Shannon, C.E., Weaver, W.: The Mathematical Theory of Information. University of Illinois Press, Urbana (1949)
Kolmogorov, A.N.: Information Theory and the Theory of Algorithms vol. 3. Kluwer, Dordrecht (1993). Selected works
Billingsley, P.: Ergodic Theory and Information. Wiley, New York (1965)
Baek, S.K., Jung, W.S., Kwon, O., Moon, H.T.: Transfer entropy analysis of the stock market. physics/0509014 (2005)
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The financial support from the funds of the State Key Laboratory of Rail Traffic Control and Safety (RCS2010ZT006), the China National Science (60772036, 61071142), and the National High Technology Research Development Program of China (863 Program) (2011AA110303) are gratefully acknowledged.
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Appendix
Appendix
Probability of states for (a) ShangZheng, (b) ShenCheng, (c) HSI, (d) DJI, (e) NAS, (f) S&P500 of Data B as a function of d
DCCA analysis of stock returns
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Shi, W., Shang, P. Cross-sample entropy statistic as a measure of synchronism and cross-correlation of stock markets. Nonlinear Dyn 71, 539–554 (2013). https://doi.org/10.1007/s11071-012-0680-z
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DOI: https://doi.org/10.1007/s11071-012-0680-z