On periodic GARCH processes: Stationarity, existence of moments and geometric ergodicity

This paper examines some probabilistic properties of a class of models featuring periodicity in conditional heteroskedasticity (we refer to it as the periodic GARCH process (PGARCH)). In these models, the parameters are allowed to switch between different regimes. The periodic structure in a GARCH process shares many properties with periodic ARMA process (PARMA). We examine the strict and second order periodic stationarities, the existence of higher-order moments, the covariance structure, the geometric ergodicity and β-mixing of the PGARCH(p, q) process under general and tractable assumptions. Some examples are proposed to illustrate the various concepts.