Estimation of Hurst exponent revisited

The bias-corrected version of R/S estimator is proposed, which 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.

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 215 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.