Ergodicity and existence of moments for local mixtures of linear autoregressions

We consider a class of nonlinear time series expressed as a local mixture of a finite number of linear autoregressions. The mixing weights are continuous functions of lagged observations while the densities of the innovation terms in each autoregression can be very general and are only assumed to possess finite moments of some order. We focus on the probabilistic properties of the model and provide mild sufficient conditions for geometric ergodicity and existence of moments.