PROBABILISTIC PROPERTIES OF A MARKOV-SWITCHING PERIODIC GARCH PROCESS

In this paper, we propose an extension of a periodic GARCH (PGARCH) model to a Markov-switching periodic GARCH (MS-PGA RCH), and provide some probabilistic properties of this class of models. In particular, we address the question of strictly periodically and of weakly periodically stationary solutions. We establish necessary and sufficient conditions ensuring the existence of higher order moments. We further provide closed-form expressions for calculating the even-order moments as well as the autocovariances of the powers of a MS-PGARCH process. We thus show how these moments and autocovariances can be used for estimating model parameters using GMM method.