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On Hurst exponent estimation under heavy-tailed distributions

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  • Jozef Barunik
  • Ladislav Kristoufek

Abstract

In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal detrended fluctuation analysis (MF-DFA), detrending moving average (DMA) and generalized Hurst exponent approach (GHE) estimate Hurst exponent on independent series with different heavy tails. For this purpose, we generate independent random series from stable distribution with stability exponent {\alpha} changing from 1.1 (heaviest tails) to 2 (Gaussian normal distribution) and we estimate the Hurst exponent using the different methods. R/S and GHE prove to be robust to heavy tails in the underlying process. GHE provides the lowest variance and bias in comparison to the other methods regardless the presence of heavy tails in data and sample size. Utilizing this result, we apply a novel approach of the intraday time-dependent Hurst exponent and we estimate the Hurst exponent on high frequency data for each trading day separately. We obtain Hurst exponents for S&P500 index for the period beginning with year 1983 and ending by November 2009 and we discuss the surprising result which uncovers how the market's behavior changed over this long period.

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File URL: http://arxiv.org/pdf/1201.4786
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Paper provided by arXiv.org in its series Papers with number 1201.4786.

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Date of creation: Jan 2012
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Publication status: Published in Physica A: Statistical Mechanics and its Applications (2010), 389 (18), pp. 3844-3855
Handle: RePEc:arx:papers:1201.4786

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  1. Mielniczuk, J. & Wojdyllo, P., 2007. "Estimation of Hurst exponent revisited," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4510-4525, May.
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  3. Ellis, Craig, 2007. "The sampling properties of Hurst exponent estimates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 159-173.
  4. John T. Barkoulas & Christopher F. Baum & Nickolaos Travlos, 1996. "Long Memory in the Greek Stock Market," Boston College Working Papers in Economics 356., Boston College Department of Economics.
  5. Weron, Rafał, 2002. "Estimating long-range dependence: finite sample properties and confidence intervals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 285-299.
  6. Fabrizio Lillo & J. Doyne Farmer, 2003. "The long memory of the efficient market," Papers cond-mat/0311053, arXiv.org, revised Jul 2004.
  7. Czarnecki, Łukasz & Grech, Dariusz & Pamuła, Grzegorz, 2008. "Comparison study of global and local approaches describing critical phenomena on the Polish stock exchange market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6801-6811.
  8. Weron, Rafal, 1996. "Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables"," MPRA Paper 20761, University Library of Munich, Germany, revised 2010.
  9. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor and Francis Journals, vol. 1(2), pages 223-236.
  10. Alvarez-Ramirez, Jose & Alvarez, Jesus & Rodriguez, Eduardo & Fernandez-Anaya, Guillermo, 2008. "Time-varying Hurst exponent for US stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6159-6169.
  11. Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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Cited by:
  1. Kristoufek, Ladislav, 2012. "How are rescaled range analyses affected by different memory and distributional properties? A Monte Carlo study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4252-4260.
  2. Raffaello Morales & T. Di Matteo & Ruggero Gramatica & Tomaso Aste, 2011. "Dynamical Hurst exponent as a tool to monitor unstable periods in financial time series," Papers 1109.0465, arXiv.org.
  3. Ladislav Kristoufek, 2012. "Fractal Markets Hypothesis And The Global Financial Crisis: Scaling, Investment Horizons And Liquidity," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1250065-1-1.
  4. Barunik, Jozef & Aste, Tomaso & Di Matteo, T. & Liu, Ruipeng, 2012. "Understanding the source of multifractality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4234-4251.
  5. Ladislav Kristoufek & Miloslav Vosvrda, 2012. "Measuring capital market efficiency: Global and local correlations structure," Papers 1208.1298, arXiv.org.
  6. Silvio M. Duarte Queiros & Evaldo M. F. Curado & Fernando D. Nobre, 2011. "Minding impacting events in a model of stochastic variance," Papers 1102.4819, arXiv.org, revised Feb 2011.

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