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Rescaled Range Analysis and Detrended Fluctuation Analysis: Finite Sample Properties and Confidence Intervals

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  • Ladislav Krištoufek

Abstract

We focus on finite sample properties of two mostly used methods of Hurst exponent H estimation—rescaled range analysis (R/S) and detrended fluctuation analysis (DFA). Even though both methods have been widely applied on different types of financial assets, only several papers have dealt with the finite sample properties which are crucial as the properties differ significantly from the asymptotic ones. Recently, R/S analysis has been shown to overestimate H when compared to DFA. However, we show that even though the estimates of R/S are truly significantly higher than an asymptotic limit of 0.5, for random time series with lengths from 2^9 to 2^17, they remain very close to the estimates proposed by Anis & Lloyd and the estimated standard deviations are lower than the ones of DFA. On the other hand, DFA estimates are very close to 0.5. The results propose that R/S still remains useful and robust method even when compared to newer method of DFA which is usually preferred in recent literature.

Suggested Citation

  • 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.
  • Handle: RePEc:fau:aucocz:au2010_315
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    1. Matteo, T. Di & Aste, T. & Dacorogna, Michel M., 2005. "Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 827-851, April.
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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. Cao, Guangxi & Xu, Longbing & Cao, Jie, 2012. "Multifractal detrended cross-correlations between the Chinese exchange market and stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4855-4866.
    4. Ludwig O. Dittrich & Pavel Srbek, 2020. "Is Violation of the Random Walk Assumption an Exception or a Rule in Capital Markets?," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 48(4), pages 491-501, December.
    5. Teng, Yue & Shang, Pengjian, 2018. "Detrended fluctuation analysis based on higher-order moments of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 311-322.
    6. Ladislav KRISTOUFEK & Petra LUNACKOVA, 2013. "Long-term Memory in Electricity Prices: Czech Market Evidence," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 63(5), pages 407-424, November.
    7. Lin, Xiaoqiang & Fei, Fangyu, 2013. "Long memory revisit in Chinese stock markets: Based on GARCH-class models and multiscale analysis," Economic Modelling, Elsevier, vol. 31(C), pages 265-275.
    8. 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.
    9. Li, Daye & Nishimura, Yusaku & Men, Ming, 2016. "The long memory and the transaction cost in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 312-320.
    10. Kristoufek, Ladislav, 2015. "Finite sample properties of power-law cross-correlations estimators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 513-525.
    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. Li, Daye & Nishimura, Yusaku & Men, Ming, 2016. "Why the long-term auto-correlation has not been eliminated by arbitragers: Evidences from NYMEX," Energy Economics, Elsevier, vol. 59(C), pages 167-178.
    13. Horta, Paulo & Lagoa, Sérgio & Martins, Luís, 2014. "The impact of the 2008 and 2010 financial crises on the Hurst exponents of international stock markets: Implications for efficiency and contagion," International Review of Financial Analysis, Elsevier, vol. 35(C), pages 140-153.
    14. Li, Daye & Kou, Zhun & Sun, Qiankun, 2015. "The scale-dependent market trend: Empirical evidences using the lagged DFA method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 26-35.
    15. Ibarra-Valdez, C. & Alvarez, J. & Alvarez-Ramirez, J., 2016. "Randomness confidence bands of fractal scaling exponents for financial price returns," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 119-124.
    16. Ladislav Kristoufek, 2013. "Testing power-law cross-correlations: Rescaled covariance test," Papers 1307.4727, arXiv.org, revised Aug 2013.
    17. Gomes, Luís M. P. & Soares, Vasco J. S. & Gama, Sílvio M. A. & Matos, José A. O., 2018. "Long-term memory in Euronext stock indexes returns: an econophysics approach," Business and Economic Horizons (BEH), Prague Development Center, vol. 14(4), pages 862-881, August.
    18. Pavel Srbek, 2018. "Odhad Hurstova exponentu v časových řadách denních výnosů akciových indexů [Estimation of the Hurst Exponent in Time Series of Daily Returns of Stock Indices]," Politická ekonomie, Prague University of Economics and Business, vol. 2018(4), pages 508-524.

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    More about this item

    Keywords

    Rescaled range analysis; detrended fluctuation analysis; Hurst exponent; long-range dependence; confidence intervals;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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