Estimation of Hurst exponent revisited

  • Authors:
  • J. Mielniczuk;P. Wojdyłło

  • Affiliations:
  • Institute of Computer Science, Polish Academy of Sciences, Ordona 21, 01-237 Warsaw, Poland and Warsaw University of Technology, Plac Politechniki 1, 00-601 Warsaw, Poland;Institute of Computer Science, Polish Academy of Sciences, Ordona 21, 01-237 Warsaw, Poland and Institute of Mathematics, Polish Academy of Sciences, niadeckich 8, 00-950 Warsaw, Poland

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2007

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Abstract

In order to estimate the Hurst exponent of long-range dependent time series numerous estimators such as based e.g. on rescaled range statistic (R/S) or detrended fluctuation analysis (DFA) are traditionally employed. Motivated by empirical behaviour of the bias of R/S estimator, its bias-corrected version is proposed. It has smaller mean squared error than DFA and behaves comparably to wavelet estimator for traces of size as large as 2^1^5 drawn from some commonly considered long-range dependent processes. It is also shown that several variants of R/S and DFA estimators are possible depending on the way they are defined and that they differ greatly in their performance.