Effects of trends and seasonalities on robustness of the Hurst parameter estimators

Long-range dependence (LRD) is discovered in time series arising from different fields, especially in network traffic and econometrics. Detecting the presence and the intensity of LRD plays a crucial role in time-series analysis and fractional system identification. The existence of LRD is usually indicated by the Hurst parameters. Up to now, many Hurst parameter estimators have been proposed in order to identify the LRD property involved in a time series. Since different estimators have different accuracy and robustness performances, in this study, 13 most popular Hurst parameter estimators are summarised and their estimation performances are investigated. LRD processes with known Hurst parameters are generated as the control data set for the robustness evaluation. In addition, three types of LRD processes are also obtained as the test signals by adding noises in terms of means, trends and seasonalities to the control data set. All 13 Hurst parameter estimators are applied to these LRD processes to estimate the existing Hurst parameters. The estimation results are documented and quantified by the standard errors. Conclusions of the accuracy and robustness performances of the estimators are drawn by comparing the estimation results.