Autocovariance structure of powers of switching-regime ARMA processes

In Francq and Zakoïan, we derived stationarity conditions for ARMA(p,q) models subject to Markov switching. In this paper, we show that, under appropriate moment conditions, the powers of the stationary solutions admit weak ARMA representations, which we are able to characterize in terms of p, q, the coefficients of the model in each regime, and the transition probabilities of the Markov chain. These representations are potentially useful for statistical applications.