On periodic ergodicity of a general periodic mixed Poisson autoregression

We propose a general class of non-linear mixed Poisson autoregressions whose form and parameters are periodic over time. Under a periodic contraction condition on the forms of the conditional mean, we show the existence of a unique nonanticipative solution to the model, which is strictly periodically stationary, periodically ergodic and periodically weakly dependent having in the pure Poisson case finite moments of any (integer) order. Applications to some well-known integer-valued time series models are considered.