Asymptotic Stationarity of Markov-Switching Time-Frequency Garch Processes

Conditions for asymptotic wide-sense stationarity of generalized autoregressive conditional heteroscedasticity (GARCH) processes with regime-switching are necessary for ensuring finite second moments. In this paper, we introduce a stationarity analysis for the Markov-switching time-frequency GARCH (MSTF-GARCH) model which has been recently introduced for modeling nonstationary signals in the time-frequency domain. We obtain a recursive vector form for the unconditional variance by using a representative matrix which is constructed from both the GARCH parameters of each regime, and the regimes´ transition probabilities. We show that constraining the spectral radius of that matrix to be less than one is both necessary and sufficient for asymptotic wide-sense stationarity. The generated matrix is also shown to be useful for deriving the asymptotic covariance matrix of the process