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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.

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Bibliographic Info

Article provided by Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies in its journal AUCO Czech Economic Review.

Volume (Year): 4 (2010)
Issue (Month): 3 (November)
Pages: 315-329

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Handle: RePEc:fau:aucocz:au2010_315

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Related research

Keywords: Rescaled range analysis; detrended fluctuation analysis; Hurst exponent; long-range dependence; confidence intervals;

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  1. T. Di Matteo & T. Aste & Michel M. Dacorogna, 2005. "Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development," Econometrics 0503004, EconWPA.
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Cited by:
  1. Ladislav Kristoufek & Miloslav Vosvrda, 2012. "Measuring capital market efficiency: Global and local correlations structure," Papers 1208.1298, arXiv.org.
  2. 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.
  3. Ladislav Kristoufek & Petra Lunackova, 2013. "Long-term memory in electricity prices: Czech market evidence," Papers 1309.0582, arXiv.org.
  4. Ladislav Kristoufek, 2013. "Testing power-law cross-correlations: Rescaled covariance test," Papers 1307.4727, arXiv.org, revised Aug 2013.
  5. 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.
  6. Ladislav Kristoufek, 2014. "Leverage effect in energy futures," Papers 1403.0064, arXiv.org.

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