Extended linear var representations of markov switching varma models

We develop a unified and general framework for the analysis of Markov switching models by extending the existing methodology to the most general setting of Markov switching VARMA(p, q) processes. Our approach is based on representing such models as extended linear non-Gaussian VAR(1) systems, which facilitates the derivation of closed-form matrix expressions for the moments of the considered process and its powers. We provide explicit formulas for higher order moments conditional on the regime distribution, and define non linear conditional responses - expressed as expectations of higher-order moments - which serve to derive forecasting and impulse response functions. These contributions significantly generalize previous results limited to MS VAR(1) settings.