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Zbl 1162.62404
Mielniczuk, J.; Wojdyłło, P.
Estimation of Hurst exponent revisited. (English)
[J] Comput. Stat. Data Anal. 51, No. 9, 4510-4525 (2007). ISSN 0167-9473

Summary: 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 $2^{15}$ 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.

MSC 2000:: *62M10 Time series, etc. (statistics)
62F10 Point estimation
65T60 Wavelets
62G05 Nonparametric estimation

Keywords: detrended fluctuation analysis (DFA) estimator; long-range dependence; rescaled adjusted range statistic (R/S); scaling property; wavelet estimator

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Zentralblatt MATH Berlin [Germany]