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. in statistics (GARCH) |
| 62F10 | Point estimation |
| 65T60 | Numerical methods for wavelets |
| 62G05 | Nonparametric estimation |
Keywords:
detrended fluctuation analysis (DFA) estimator; long-range dependence; rescaled adjusted range statistic (R/S); scaling property; wavelet estimatorReferences:
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