How are rescaled range analyses affected by different memory and distributional properties? A Monte Carlo study
In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlations detection - classical and modified rescaled range analyses. A focus is put on an effect of different distributional properties on an ability of the methods to efficiently distinguish between short and long-term memory. To do so, we analyze the behavior of the estimators for independent, short-range dependent, and long-range dependent processes with innovations from 8 different distributions. We find that apart from a combination of very high levels of kurtosis and skewness, both estimators are quite robust to distributional properties. Importantly, we show that R/S is biased upwards (yet not strongly) for short-range dependent processes, while M-R/S is strongly biased downwards for long-range dependent processes regardless of the distribution of innovations.
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Andrew W. Lo, 1989.
"Long-term Memory in Stock Market Prices,"
NBER Working Papers
2984, National Bureau of Economic Research, Inc.
- Barunik, Jozef & Kristoufek, Ladislav, 2010.
"On Hurst exponent estimation under heavy-tailed distributions,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 389(18), pages 3844-3855.
- Jozef Barunik & Ladislav Kristoufek, 2012. "On Hurst exponent estimation under heavy-tailed distributions," Papers 1201.4786, arXiv.org.
- 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.
- 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.
- Lillo Fabrizio & Farmer J. Doyne, 2004.
"The Long Memory of the Efficient Market,"
Studies in Nonlinear Dynamics & Econometrics,
De Gruyter, vol. 8(3), pages 1-35, September.
- Sadegh Movahed, M. & Hermanis, Evalds, 2008. "Fractal analysis of river flow fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 915-932.
- Chen, Chien-chih & Lee, Ya-Ting & Chang, Young-Fo, 2008. "A relationship between Hurst exponents of slip and waiting time data of earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(18), pages 4643-4648.
- Ladislav Krištoufek, 2010. "Rescaled Range Analysis and Detrended Fluctuation Analysis: Finite Sample Properties and Confidence Intervals," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 4(3), pages 315-329, November.
- John Barkoulas & Christopher Baum & Nickolaos Travlos, 2000.
"Long memory in the Greek stock market,"
Applied Financial Economics,
Taylor & Francis Journals, vol. 10(2), pages 177-184.
- R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
- 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.
- Enrico Onali & John Goddard, 2014.
"Are European equity markets efficient? New evidence from fractal analysis,"
- Onali, Enrico & Goddard, John, 2011. "Are European equity markets efficient? New evidence from fractal analysis," International Review of Financial Analysis, Elsevier, vol. 20(2), pages 59-67, April.
- Couillard, Michel & Davison, Matt, 2005. "A comment on measuring the Hurst exponent of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 404-418.
- T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 21-36.
- Ellis, Craig, 2007. "The sampling properties of Hurst exponent estimates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 159-173.
- Matos, José A.O. & Gama, Sílvio M.A. & Ruskin, Heather J. & Sharkasi, Adel Al & Crane, Martin, 2008. "Time and scale Hurst exponent analysis for financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3910-3915.
- José, Marco V. & Govezensky, Tzipe & Bobadilla, Juan R., 2005. "Statistical properties of DNA sequences revisited: the role of inverse bilateral symmetry in bacterial chromosomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 477-498.
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