On some probabilistic properties of periodic GARCH processes

This paper examines some probabilistic properties of the class of periodic GARCH processes (PGARCH) which feature periodicity in conditional heteroskedasticity. In these models, the parameters are allowed to switch between different regimes, so that their structure 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 -mixing of the PGARCH(p,q) process under general and tractable assumptions. Some examples are proposed to illustrate the various concepts.