Local asymptotic normality in periodic threshold GARCH and periodic GARCH models

In this article, we derive the local asymptotic normality (LAN) property for periodic GARCH and periodic threshold GARCH models with periodically time-varying parameters. For this purpose, we adapt a framework that works under quite natural and economic conditions. This property is fundamental and prepares the way for efficient and adaptive estimation in a semiparametric setting for future consideration. The simulation experiment is carried out for studying the distribution of the likelihood ratio under different underlying error distributions.