  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.
