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On periodic ergodicity of a general periodic mixed Poisson autoregression

Aknouche, Abdelhakim and Bentarzi, Wissam and Demouche, Nacer (2017): On periodic ergodicity of a general periodic mixed Poisson autoregression.

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Abstract

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 higher-order moments. Applications to some well-known integer-valued time series models are considered.

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