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On periodic ergodicity of a general periodic mixed Poisson autoregression

Abdelhakim Aknouche, Wissam Bentarzi and Nacer Demouche

Statistics & Probability Letters, 2018, vol. 134, issue C, 15-21

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 moments of any (integer) order. Applications to some well-known integer-valued time series models are considered.

Keywords: Periodic mixed Poisson autoregression; Non-linear INGARCH models; Weak dependence; Strict periodic stationarity; Periodic ergodicity; Periodic contraction (search for similar items in EconPapers)
Date: 2018
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