Procesy s dlouhou pamětí a jejich vývoj ve výnosech indexu PX v letech 1999 – 2009

Kristoufek, Ladislav (2009): Procesy s dlouhou pamětí a jejich vývoj ve výnosech indexu PX v letech 1999 – 2009.

Abstract

Long-term memory processes have been extensively examined in recent literature as they provide simple way to test for predictability 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 present results of Monte Carlo simulations for rescaled range, modified rescaled range and detrended fluctuation analysis based on chosen scales taken into consideration. The results of simulations show that even independent process can show Hurst exponent far from 0.5. In our analysis of evolution of Hurst exponent between 1999 and 2009, we show that Czech PX experienced persistent behavior which weakened in time. Nevertheless, the returns of PX remain close to confidence interval separating independent and persistent behavior.

• Item Type: MPRA Paper
• English Title: Long-term memory and its evolution in returns of PX between 1999 and 2009
• Language: Czech
• Keywords: Hurst exponent, long-range dependence, time series analysis, persistence, rescaled range, detrended fluctuation analysis
• Subjects: G - Financial Economics > G1 - General Financial Markets > G14 - Information and Market Efficiency ; Event Studies ; Insider Trading; G - Financial Economics > G1 - General Financial Markets > G15 - International Financial Markets; G - Financial Economics > G1 - General Financial Markets > G10 - General

References

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.

ALPTEKIN, N. 2006. Long Memory Analysis of USD/TRL Exchange Rate, International Journal of Social Sciences. 2006, Vol. 1, No. 2.

ALVAREZ-RAMIREZ, J.; RODRIGUEZ, E.; ECHEVERRIA, J. 2005. Detrending fluctuation analysis based on moving average filtering. Physica A. 2005, Vol. 354.

BARKOULAS, J.; BAUM, CH.; TRAVLOS, N. 2000. Long memory in the Greek stock market. Applied Financial Economics. 2000, Vol. 10.

BASHAN, A.; BARTSCH, R.; KANTELHARDT, J.; HAVLIN, S. 2008. Comparison of detrending methods for fluctuation analysis. arXiv:0804.4081

BERAN, J. 1994. Statistics for Long-Memory Processes, Monographs on Statistics and Applied Probability 61. New York: Chapman & Hall, 1994. ISBN 978-0412049019.

CHIN, W. 2008. Spurious Long-range Dependence: Evidence from Malaysian Equity Markets. MPRA Paper. 2008, No. 7914.

CONT, R. 2001. Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance. 2001, Vol. 1, No. 2.

COUILLARD, M; DAVISON, M. 2005. A comment on measuring the Hurst exponent of financial time series. Physica A. 2005, Vol. 348.

DI MATTEO, T. 2007. Multi-scaling in Finance. Quantitative Finance. 2007, Vol. 7, No. 1.

DÜLGER, F.; OZDEMIR, Z. 2005. Current Account Sustainability in Seven Developed Countries. Journal of Economic and Social Research. 2005, Vol. 7, No. 2.

EICHNER, J.; KANTELHARDT, J.; BUNDE, A.; HAVLIN, S. 2007. Statistics of return intervals in long-term correlated records. Physical Review E. 2007, Vol. 75.

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.

EMBRECHTS, P.; MAEJIMA, M. 2002. Selfsimilar Processes, New Jersey: Princeton University Press, 2002. ISBN 978-0691096278.

GRECH, D.; MAZUR, Z. 2004. Can one make any crash prediction in finance using the local Hurst exponent idea? Physica A. 2004, Vol. 336.

GRECH, D.; MAZUR, Z. 2005. Statistical Properties of Old and New Techniques in Detrended Analysis of Time Series. Acta Physica Polonica B. 2005, Vol. 36, No. 8.

HU, K.; IVANOV, P.; CHEN, Z.; CARPENA, P.; STANLEY, H. 2001. Effect of trends on detrended fluctuation analysis. Physical Review E. 2001, Vol. 64.

HURST, H.E. 1951. Long term storage capacity of reservoirs. Transactions of the American Society of Engineers. 1951, Vol. 116.

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.

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.

LILLO, F.; FARMER, J. 2004. The Long Memory of the Efficient Market. Studies in Nonlinear Dynamics & Econometrics. 2004, Vol. 8, No. 3.

LO, A.; MACKINLAY, C. 1999. A Non-Random Walk Down Wall Street. New Jersey: Princeton University Press, 1999. ISBN 0-691-09256-7.

LO, A. 1991. Long-term memory in stock market prices. Econometrica. 1991, Vol. 59, No. 5.

LUX, T. 2007. Applications of Statistical Physics in Finance and Economics. Economics Working Paper, Christian-Albrechts-Universität Kiel. 2007, No 2007-05.

MANDELBROT, B.; VAN NESS, J. 1968. Fractional Brownian motions, fractional noises and applications. SIAM Review. 1968, Vol. 10, No. 422.

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.

MANDELBROT, B. 1970. Analysis of long-run dependence in economics: the R/S technique. Econometrica. 1970, Vol. 39.

MANDELBROT, B. 1972. Statistical methodology for non-periodic cycles: from covariance to R/S analysis. Annals of Economic and Social Measurement. 1972, Vol. 1.

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.

MCKENZIE, M. 2002. Non-periodic Australian Stock Market Cycles: Evidence from Rescaled Range Analysis. Economic Record. 2002, Vol. 73, No. 239.

PENG, C.; BULDYREV, S.; HAVLIN, S.; SIMONS, M.; STANLEY, H.; GOLDBERGER, A. 1994. Mosaic organization of DNA nucleotides. Physical Review E. 1994, Vol. 49, No. 2.

PETERS, E. 1994. Fractal Market Analysis – Applying Chaos Theory to Investment and Analysis. New York: John Wiley & Sons, Inc., 1994. ISBN 978-0471585244.

QUANG, T. 2007. Testing the Weak Form of Efficient Market Hypothesis for the Czech Stock Market. Politická ekonomie. 2007, Vol. 6.

SAMORODNITSKY, G. 2006. Long memory and self-similar processes. Annales de la faculté des sciences de Toulouse Mathématiques. 2006, Vol. 25, No. 1.

SAMORODNITSKY, G. 2007. Long Range Dependence, Now Publishers Inc., 2007. ISBN 978-1601980908.

TAQQU, M.; TEVEROSKY, W.; WILLINGER, W. 1995. Estimators for long-range dependence: an empirical study. Fractals. 1995, Vol. 3, No. 4.

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.

VANDEWALLE, N.; AUSLOOS, M.; BOVEROUX, PH. 1997. Detrended Fluctuation Analysis of the Foreign Exchange Market. Econophysic Workshop, Budapest, Hungary, 1997.

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.

WERON, R. 2002. Estimating long-range dependence: finite sample properties and confidence intervals. Physica A. 2002, Vol. 312.

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.