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How are rescaled range analyses affected by different memory and distributional properties? A Monte Carlo study

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  • Kristoufek, Ladislav

Abstract

In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlation 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-term memory 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 eight 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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  • 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.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:17:p:4252-4260
    DOI: 10.1016/j.physa.2012.04.005
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    1. 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.
    2. Ellis, Craig, 2007. "The sampling properties of Hurst exponent estimates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 159-173.
    3. 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.
    4. 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.
    5. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    6. 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.
    7. T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 21-36.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Kristoufek, Ladislav, 2010. "On spurious anti-persistence in the US stock indices," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 68-78.
    13. 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.
    14. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    15. 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.
    16. 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.
    17. Rehman, Shafiqur, 2009. "Study of Saudi Arabian climatic conditions using Hurst exponent and climatic predictability index," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 499-509.
    18. 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.
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    1. Ladislav Kristoufek & Miloslav Vosvrda, 2014. "Measuring capital market efficiency: long-term memory, fractal dimension and approximate entropy," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(7), pages 1-9, July.
    2. Kristoufek, Ladislav, 2014. "Leverage effect in energy futures," Energy Economics, Elsevier, vol. 45(C), pages 1-9.
    3. Benjamin R Auer, 2016. "Pure return persistence, Hurst exponents and hedge fund selection – A practical note," Journal of Asset Management, Palgrave Macmillan, vol. 17(5), pages 319-330, September.
    4. Kristoufek, Ladislav & Vosvrda, Miloslav, 2013. "Measuring capital market efficiency: Global and local correlations structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 184-193.
    5. Benjamin Rainer Auer, 2018. "Are standard asset pricing factors long-range dependent?," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 42(1), pages 66-88, January.
    6. Ladislav Kristoufek, 2013. "Testing power-law cross-correlations: Rescaled covariance test," Papers 1307.4727, arXiv.org, revised Aug 2013.
    7. David, S.A. & Inácio, C.M.C. & Quintino, D.D. & Machado, J.A.T., 2020. "Measuring the Brazilian ethanol and gasoline market efficiency using DFA-Hurst and fractal dimension," Energy Economics, Elsevier, vol. 85(C).
    8. Hull, Matthew & McGroarty, Frank, 2014. "Do emerging markets become more efficient as they develop? Long memory persistence in equity indices," Emerging Markets Review, Elsevier, vol. 18(C), pages 45-61.
    9. Anagnostidis, P. & Varsakelis, C. & Emmanouilides, C.J., 2016. "Has the 2008 financial crisis affected stock market efficiency? The case of Eurozone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 116-128.
    10. Zunino, Luciano & Bariviera, Aurelio F. & Guercio, M. Belén & Martinez, Lisana B. & Rosso, Osvaldo A., 2016. "Monitoring the informational efficiency of European corporate bond markets with dynamical permutation min-entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 1-9.
    11. Auer, Benjamin R., 2016. "On the performance of simple trading rules derived from the fractal dynamics of gold and silver price fluctuations," Finance Research Letters, Elsevier, vol. 16(C), pages 255-267.
    12. Auer, Benjamin R., 2016. "On time-varying predictability of emerging stock market returns," Emerging Markets Review, Elsevier, vol. 27(C), pages 1-13.
    13. Kristoufek, Ladislav & Vosvrda, Miloslav, 2014. "Commodity futures and market efficiency," Energy Economics, Elsevier, vol. 42(C), pages 50-57.
    14. Kristoufek, Ladislav, 2019. "Are the crude oil markets really becoming more efficient over time? Some new evidence," Energy Economics, Elsevier, vol. 82(C), pages 253-263.
    15. Auer, Benjamin R. & Hoffmann, Andreas, 2016. "Do carry trade returns show signs of long memory?," The Quarterly Review of Economics and Finance, Elsevier, vol. 61(C), pages 201-208.

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