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.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Periodic mixed Poisson autoregression, periodic INGARCH models, non-linear INGARCH models, weak dependence, strict periodic stationarity, periodic ergodicity, periodic contraction condition.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C19 - Other; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium

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