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Keywords:
Markov-switching models; periodic $GARCH$ models; periodic stationarity; higher-order moments; Markov-switching $PGARCH$ models; $GMM$ method
Markov-switching models; periodic $GARCH$ models; periodic stationarity; higher-order moments; Markov-switching $PGARCH$ models; $GMM$ method
Summary:
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.
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