Robustness Analysis of the Estimators for Noisy Long-Range Dependent Time Series

Abstract

Processes with long-range correlations or called long-range dependent (LRD) processes are all around us in nature. The presence and nature of LRD is characterized by the Hurst parameter (0 < H < 1). The aim of this paper is to make a practical analysis of the robustness of the Hurst parameter estimators. A simple model of exactly self-similar process-Fractional Gaussian noise (FGN) with parameter H ∈ (0, 1) is applied to evaluate Hurst parameter estimators. The white Gaussian noise or the Symmetric α-stable (SαS) noise is superimposed in order to evaluate the reliability and the robustness of different estimators. In this paper, six statistic analysis methods, R/S statistic, Aggregated Variance method, Absolute Value method, Residuals of Regression method, Periodogram method, and Whittle method are analyzed. It follows from the comparison that the Variance of Residuals method is almost unbiased for non-noise LRD processes. And the Whittle method has best robustness to Symmetric α-stable (SαS) noisy LRD processes. The robustness analysis has practical value for analyzing noisy LRD time series, especially for the economic data, under water signal, biomedical signal and the communication signal which are corrupted by impulsive noise.