Local asymptotic normality for a periodically time varying long memory parameter

Abstract

A periodically time varying long memory parameter version of the fixed long memory parameter case local asymptotic normality (LAN) results are implemented here. The process is assumed to be invertible and causal for simplicity. We prove that the general condition of LAN is verified by our model. The simulation experiment is carried out for studying the distribution of the central sequence in LAN property. The most interesting in this note is to construct an adaptive estimate in future consideration of this type of model.