Bias Comparison on Memory Parameter of Skip Sampled Long Memory and Exponentially Smooth Transition Autoregressive Process

Abstract

This research investigates the bias of the memory parameter of two aggregated processes i.e. long memory and Exponentially Smooth Transition Autoregressive (ESTAR), estimated by GPH estimator. Intensive simulation study has been carried out in order to identify the patterns generated by the simulation processes. It turns out that the bias of memory parameter of the skip sampled long memory process consistently increases by increasing the sampling interval only for short sampling intervals, while memory of the ESTAR process changes irregularly with increasing the sampling interval. Moreover, the memory parameters lies in the region of long memory process for true long memory, while memory parameter of ESTAR frequently biased towards short memory process. These facts thus can be considered as a simple procedure for discriminating long memory with ESTAR.