Politická ekonomie 2010, 58(4):471-487 | DOI: 10.18267/j.polek.742

Dlouhá paměť a její vývoj ve výnosech burzovního indexu PX v letech 1997-2009

Ladislav Krištoufek
IES FSV Univerzity Karlovy v Praze a ÚTIA Akademie věd ČR.

Long-Term Memory and Its Evolution in Returns of Stock Index PX Between 1997 and 2009

Long-term memory processes have been extensively examined in recent literature as they provide simple way to test for predictabilty in the underlying process. However, most of the literature interprets the results of estimated Hurst exponent simply by its comparison to its asymptotic limit of 0.5. Therefore, we use moving block bootstrap method for rescaled range and periodogram method. In our analysis of evolution of Hurst exponent between 1997 and 2009, we show that PX experienced persistent behavior which weakened in time. Nevertheless, the returns of PX remain close to confidence interval separating independent and persistent behavior.

Keywords: time series analysis, econophysics, long-range dependence, rescaled range, periodogram
JEL classification: G1, G10, G14, G15

Published: August 1, 2010  Show citation

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Krištoufek, L. (2010). Long-Term Memory and Its Evolution in Returns of Stock Index PX Between 1997 and 2009. Politická ekonomie, 58(4), 471-487. doi: 10.18267/j.polek.742
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    References

    1. ALFI, V.; COCCETTI, F.; MAROTTA, M.; PETRI, A; PIETRONERO, L. 2008. Exact Results for the Roughness of a Finite Size Random Walk. Physica A. 2008, Vol. 370, No. 1. Go to original source...
    2. ALPTEKIN, N. 2006. Long Memory Analysis of USD/TRL Exchange Rate, International Journal of Social Sciences. 2006, Vol. 1, No. 2.
    3. ALVAREZ-RAMIREZ, J.; RODRIGUEZ, E.; ECHEVERRIA, J. 2005. Detrending fluctuation analysis based on moving average filtering. Physica A. 2005, Vol. 354. Go to original source...
    4. BARKOULAS, J.; BAUM, CH.; TRAVLOS, N. 2000. Long memory in the Greek stock market. Applied Financial Economics. 2000, Vol. 10. Go to original source...
    5. BARUNÍK. 2008. How Do Neural Networks Enhance the Predictability of Central European Stock Returns? Finance a úvěr - Czech Journal of Economics and Finance. 2008, Vol. 58, No. 7-8.
    6. BASHAN, A.; BARTSCH, R.; KANTELHARDT, J.; HAVLIN, S. 2008. Comparison of detrending methods for fluctuation analysis. arXiv:0804.4081 Go to original source...
    7. BERAN, J. 1994. Statistics for Long-Memory Processes, Monographs on Statistics and Applied Probability 61. New York: Chapman & Hall, 1994. ISBN 978-0412049019.
    8. CAJUEIRO, D.; TABAK, B. 2006. Testing for predictability in equity returns for European transition markets. Economic Systems. 2006, Vol. 30. Go to original source...
    9. CONT, R. 2001. Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance. 2001, Vol. 1, No. 2. Go to original source...
    10. COUILLARD, M; DAVISON, M. 2005. A comment on measuring the Hurst exponent of financial time series. Physica A. 2005, Vol. 348. Go to original source...
    11. DI MATTEO, T. 2007. Multi-scaling in Finance. Quantitative Finance. 2007, Vol. 7, No. 1. Go to original source...
    12. DIVIŠ, K.; TEPLÝ, P. 2005. Informační efektivnost burzovních trhů ve střední Evropě. Finance a úvěr - Czech Journal of Economics and Finance. 2005, Vol. 55, No. 9-10.
    13. DÜLGER, F.; OZDEMIR, Z. 2005. Current Account Sustainability in Seven Developed Countries. Journal of Economic and Social Research. 2005, Vol. 7, No. 2.
    14. EFRON, B. 1979. Bootstrap methods: Another look at the jackknife. Annals of Statistics. 1979, Vol. 7. Go to original source...
    15. EICHNER, J.; KANTELHARDT, J.; BUNDE, A.; HAVLIN, S. 2007. Statistics of return intervals in longterm correlated records. Physical Review E. 2007, Vol. 75. Go to original source...
    16. EINSTEIN, A.; WU, H.-S.; GIL, J. 2001. Detrended fluctuation analysis of chromatin texture for diagnosis in breast cytology. Fractals. 2001, Vol. 9, No. 4.
    17. EMBRECHTS, P.; MAEJIMA, M. 2002. Selfsimilar Processes, New Jersey: Princeton University Press, 2002. ISBN 978-0691096278. Go to original source...
    18. GEWEKE, J.; PORTER-HUDAK, S. 1983. The estimation and application of long memory time series models. Journal of Time Series Analysis. 1983, Vol. 4, No. 4. Go to original source...
    19. GRECH, D.; MAZUR, Z. 2004. Can one make any crash prediction in finance using the local Hurst exponent idea? Physica A. 2004, Vol. 336. Go to original source...
    20. HÁJEK, J. 2007. Test slabé formy efektivnosti středoevropských akciových trhů. Politická ekonomie. 2007, Vol. 55, No. 6, pp. 773-791. Go to original source...
    21. HURST, H. E. 1951. Long term storage capacity of reservoirs. Transactions of the American Society of Engineers. 1951, Vol. 116. Go to original source...
    22. JANDA, K. 1994. Modelling Risks of Share Portfolio (in Czech with English summary). Finance a úvěr. 1994, Vol. 44, No. 9.
    23. JANDA, K.; SVÁROVSKÁ, B. 2009. Investing into Microfinance Investment Funds. Working Papers IES 2009/32, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies. 2009.
    24. JANDA, K.; SVÁROVSKÁ, B. 2009. Investing into Microfinance. Journal of Business Economics and Management. 2010 forthcoming, Vol. 10.
    25. JARQUE, C.; BERA, A. 1981. Efficient tests for normality, homoscedasticity and serial independence of regression residuals: Monte Carlo evidence. Economics Letters. 1981, Vol. 7, No. 4. Go to original source...
    26. KRIŠTOUFEK, L. 2009. Classical and modified rescaled range analysis: Sampling properties under heavy tails. Working Papers IES 2009/26, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies. 2009.
    27. KWIATKOWSKI, D.; PHILLIPS, P.; SCHMIDT, P.; SHIN, Y. 1992. Testing the null of stationarity against the alternative of a unit root: How sure are we that the economic time series have a unit root? Journal of Econometrics. 1992, Vol. 54. Go to original source...
    28. LILLO, F.; FARMER, J. 2004. The Long Memory of the Efficient Market. Studies in Nonlinear Dynamics & Econometrics. 2004, Vol. 8, No. 3. Go to original source...
    29. LO, A.; MACKINLAY, C. 1999. A Non-Random Walk Down Wall Street. New Jersey: Princeton University Press, 1999. ISBN 0-691-09256-7.
    30. LO, A. 1991. Long-term memory in stock market prices. Econometrica. 1991, Vol. 59, No. 5. Go to original source...
    31. LUX, T. 2007. Applications of Statistical Physics in Finance and Economics. Economics Working Paper, Christian-Albrechts-Universität Kiel. 2007, No 2007-05.
    32. MANDELBROT, B.; VAN NESS, J. 1968. Fractional Brownian motions, fractional noises and applications. SIAM Review. 1968, Vol. 10, No. 422. Go to original source...
    33. MANDELBROT, B.; WALLIS, R. 1969. Robustness of the rescaled range R/S in the measurement of noncyclic long-run statistical dependence. Water Resources Research. 1999, Vol. 5. Go to original source...
    34. MANDELBROT, B. 1970. Analysis of long-run dependence in economics: the R/S technique. Econometrica. 1970, Vol. 39.
    35. MANDELBROT, B. 1972. Statistical methodology for non-periodic cycles: from covariance to R/S analysis. Annals of Economic and Social Measurement. 1972, Vol. 1.
    36. MATOS, J.; GAMA, S.; RUSKIN, H.; SHARKASI, A.; CRANE, M. 2008. Time and scale Hurst exponent analysis for financial markets. Physica A. 2008, Vol. 387, No. 15. Go to original source...
    37. MCKENZIE, M. 2002. Non-periodic Australian Stock Market Cycles: Evidence from Rescaled Range Analysis. Economic Record. 2002, Vol. 73, No. 239. Go to original source...
    38. PETERS, E. 1994. Fractal Market Analysis - Applying Chaos Theory to Investment and Analysis. New York: John Wiley & Sons, Inc., 1994. ISBN 978-0471585244.
    39. SAMORODNITSKY, G. 2006. Long Range Dependence, Now Publishers Inc., 2007. ISBN 978-1601980908. Go to original source...
    40. SRINIVAS, V.; SRINIVASAN, K.. 2000. Post-blackening approach for modeling dependent annual streamflows. Journal of Hydrology. 2000, Vol. 230. Go to original source...
    41. TAQQU, M.; TEVEROSKY, W.; WILLINGER, W. 1995. Estimators for long-range dependence: an empirical study. Fractals. 1995, Vol. 3, No. 4. Go to original source...
    42. TEVEROVSKY, V.; TAQQU, M.; WILLINGER, W. 1999. A critical look at Lo's modified R/S statistic. Journal of Statistical Planning and Inference. 1999, Vol. 80, No. 1-2. Go to original source...
    43. TRAN, Q. 2007. Testing the Weak Form of Efficient Market Hypothesis for the Czech Stock Market. Politická ekonomie. 2007, Vol. 55, No. 6, pp. 751-772. Go to original source...
    44. TRAN, Q. 2005. The Fractal Market Analysis and Its Application on Czech Conditions. Acta Oeconomica Pragensia. 2005, Vol. 13., No. 1. Go to original source...
    45. VANDEWALLE, N.; AUSLOOS, M.; BOVEROUX, PH. 1997. Detrended Fluctuation Analysis of the Foreign Exchange Market. Econophysic Workshop, Budapest, Hungary, 1997.
    46. WANG, W.; VAN GELDER, P.; VRIJLING, J.; CHEN, X. 2006. Detecting long-memory: Monte Carlo simulations and application to daily streamflow processess. Hydrology and Earth System Sciences Discussions. 2006, Vol. 3. Go to original source...
    47. WERON, R. 2002. Estimating long-range dependence: finite sample properties and confidence intervals. Physica A. 2002, Vol. 312. Go to original source...
    48. WERON, R. 2001. Measuring long-range dependence in electricity prices. arXiv:cond-mat/0103621v1.
    49. ZHUANG, Y.; GREEN, CH.; MAGGIONI, P. 2000. The Great Rebound, The Great Crash, and Persistence in British Stock Prices. Economic Research Paper, Loughborough University. 2000, No. 00/11.

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