Strong consistency and asymptotic normality of least squares estimators for PGARCH and PARMA-PGARCH models

This paper deals with the probabilistic structure and the asymptotic properties of parameters least squares estimates (LSE) for periodic GARCH (PGARCH) and for PARMA-PGARCH models. In this class of models, the parameters are allowed to switch between different regimes. Firstly, we give necessary and sufficient conditions ensuring the existence of stationary solutions (in a periodic sense) and for the existence of moments of any order. Secondly, a least squares estimation approach for estimating PGARCH and PARMA-PGARCH models are discussed. The strong consistency and the asymptotic normality of the estimators are studied given mild regularity conditions, requiring strict stationarity and the finiteness of moments of some order for the errors term.