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ERGODIC PROPERTIES OF PERIODIC INTEGER-VALUED GARCH MODELS
Keywords:
integer-valued time series models, periodic INGARCH model, periodic stationarity, ergodic properties, Lipschitz conditional mean.DOI:
https://doi.org/10.17654/0972361722004Abstract
We propose general and tractable periodic ergodicity conditions for a general class of integer-valued GARCH (generalized autoregressive conditionally heteroskedastic, INGARCH) models with periodic time-varying conditional mean parameters. The conditional distributions of the periodic INGARCH model are assumed to belong to the class of distributions with equal conditional stochastic and mean orders, which includes in particular the one-parameter exponential family and other interesting distributions. An extension to periodic INGARCH models with nonlinear Lipschitz conditional means is also provided. The results apply to many specific periodic INGARCH models such as the Poisson periodic INGARCH, the negative binomial periodic INGARCH and the zero-inflated Poisson or negative binomial INGARCH models.
Received: November 8, 2021
Accepted: December 13, 2021
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