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

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  • Ladislav Kristoufek

Abstract

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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  • Ladislav Kristoufek, 2012. "How are rescaled range analyses affected by different memory and distributional properties? A Monte Carlo study," Papers 1201.3511, arXiv.org.
  • Handle: RePEc:arx:papers:1201.3511
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    10. 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.
    11. T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 21-36.
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    Cited by:

    1. Kristoufek, Ladislav, 2014. "Leverage effect in energy futures," Energy Economics, Elsevier, vol. 45(C), pages 1-9.
    2. Ladislav Kristoufek, 2013. "Testing power-law cross-correlations: Rescaled covariance test," Papers 1307.4727, arXiv.org, revised Aug 2013.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Ladislav Kristoufek, 2018. "Are the Crude Oil Markets Really Becoming More Efficient over Time? Some New Evidence," Working Papers IES 2018/07, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Feb 2018.
    8. repec:pal:assmgt:v:17:y:2016:i:5:d:10.1057_jam.2016.7 is not listed on IDEAS
    9. Kristoufek, Ladislav & Vosvrda, Miloslav, 2014. "Commodity futures and market efficiency," Energy Economics, Elsevier, vol. 42(C), pages 50-57.
    10. repec:spr:jecfin:v:42:y:2018:i:1:d:10.1007_s12197-017-9385-y is not listed on IDEAS
    11. 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.
    12. 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.
    13. Auer, Benjamin R., 2016. "On time-varying predictability of emerging stock market returns," Emerging Markets Review, Elsevier, vol. 27(C), pages 1-13.
    14. 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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