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Procesy s dlouhou pamětí a jejich vývoj ve výnosech indexu PX v letech 1999 – 2009
[Long-term memory and its evolution in returns of PX between 1999 and 2009]

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  • Kristoufek, Ladislav

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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 16435.

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Date of creation: 08 Jul 2009
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Handle: RePEc:pra:mprapa:16435

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Keywords: Hurst exponent; long-range dependence; time series analysis; persistence; rescaled range; detrended fluctuation analysis;

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  1. Grech, D & Mazur, Z, 2004. "Can one make any crash prediction in finance using the local Hurst exponent idea?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 133-145.
  2. Rafal Weron, 2001. "Estimating long range dependence: finite sample properties and confidence intervals," HSC Research Reports HSC/01/03, Hugo Steinhaus Center, Wroclaw University of Technology.
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  9. McKenzie, Michael D, 2001. "Non-periodic Australian Stock Market Cycles: Evidence from Rescaled Range Analysis," The Economic Record, The Economic Society of Australia, vol. 77(239), pages 393-406, December.
  10. Fabrizio Lillo & J. Doyne Farmer, 2003. "The long memory of the efficient market," Papers cond-mat/0311053, arXiv.org, revised Jul 2004.
  11. Thomas Lux, 2008. "Applications of Statistical Physics in Finance and Economics," Kiel Working Papers 1425, Kiel Institute for the World Economy.
  12. Tran Van Quang, 2007. "Testing the weak form of efficient market hypothesis for the czech stock market," Politická ekonomie, University of Economics, Prague, vol. 2007(6), pages 751-772.
  13. Alvarez-Ramirez, Jose & Rodriguez, Eduardo & Carlos Echeverría, Juan, 2005. "Detrending fluctuation analysis based on moving average filtering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 199-219.
  14. Chin, Wencheong, 2008. "Spurious long-range dependence: evidence from Malaysian equity markets," MPRA Paper 7914, University Library of Munich, Germany.
  15. B. Mandelbrot, 1972. "Statistical Methodology For Nonperiodic Cycles: From The Covariance To Rs Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290 National Bureau of Economic Research, Inc.
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