Periodic stationarity of random coefficient periodic autoregressions

This paper studies periodic stationarity of a random coefficient periodic autoregression (RCPAR)(RCPAR) which generalizes the standard random coefficient autoregressive (RCAR)(RCAR) model to the case where the deterministic parameters and the disturbance variances are periodically time-varying. Sufficient conditions for the existence of a (strictly and second-order) periodically stationary solution to the RCPARRCPAR equation are proposed. As an application, we study periodic stationarity of a class of periodic bilinear models and a periodic autoregression with periodic ARCHARCH errors.