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Estimation of Hurst exponent revisited. (English) Zbl 1162.62404
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:
 62M10 Time series, auto-correlation, regression, etc. (statistics) 62F10 Point estimation 65T60 Wavelets (numerical methods) 62G05 Nonparametric estimation
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