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Estimating long-range dependence in time series: An evaluation of estimators implemented in R

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Abstract

Recent studies have shown that many physiological and behavioral processes can be characterized by long-range correlations. The Hurst exponent H of fractal analysis and the fractional-differencing parameter d of the ARFIMA methodology are useful for capturing serial correlations. In this study, we report on different estimators of H and d implemented in R, a popular and freely available software package. By means of Monte Carlo simulations, we analyzed the performance of (1) the Geweke—Porter-Hudak estimator, (2) the approximate maximum likelihood algorithm, (3) the smoothed periodogram approach, (4) the Whittle estimator, (5) rescaled range analysis, (6) a modified periodogram, (7) Higuchi’s method, and (8) detrended fluctuation analysis. The findings—confined to ARFIMA (0, d, 0) models and fractional Gaussian noise—identify the best estimators for persistent and antipersistent series. Two examples combining these results with the step-by-step procedure proposed by Delignières et al. (2006) demonstrate how this evaluation can be used as a guideline in a typical research situation.

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Authors and Affiliations

  1. Department of Psychology, University of Heidelberg, Hauptstr. 47-51, 69117, Heidelberg, Germany

    Esther Stroe-Kunold, Tetiana Stadnytska, Joachim Werner & Simone Braun

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  1. Esther Stroe-Kunold
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  2. Tetiana Stadnytska
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  3. Joachim Werner
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  4. Simone Braun
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Correspondence to Joachim Werner.

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The research for this article was supported by a scholarship awarded the first author by the German National Academic Foundation. Part of this work was done while the first author was a visiting scholar with Eric-Jan Wagenmakers at the University of Amsterdam.

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Stroe-Kunold, E., Stadnytska, T., Werner, J. et al. Estimating long-range dependence in time series: An evaluation of estimators implemented in R. Behavior Research Methods 41, 909–923 (2009). https://doi.org/10.3758/BRM.41.3.909

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