Robustness of whittle-type estimators for time series with long-range dependence

Abstract

We study the robustness of the “standard Whittle ”, “local Whittle” and “aggregated Whittle” estimators by using a large number of simulated Gaussian time series with long-range dependence. We also consider what happens when the Gaussian innovations are replaced by infinite variance symmetric stable ones. The standard Whittle estimator is a parametric estimator, the local Whittle estimator is a semi-parametric one recently developed by Robinson (1995) and the aggregated Whittle estimator smoothes out the high frequencies. The goal is to estimate H, the intensity of long-range dependence. We investigate the standard deviation and bias of these estimators in order to determine when they are reliable. These estimators are then applied to real-life Ethernet data