Estimation of Hurst exponent revisited

In order to estimate the Hurst exponent of long-range dependent time series numerous estimators such as based e.g. on rescaled 9 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 11 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 13 greatly in their performance.