Integer-Valued Autoregressive Models With Survival Probability Driven By A Stochastic Recurrence Equation

This paper proposes a new class of integer-valued autoregressive models with a dynamic survival probability. The peculiarity of this class of models lies in the specification of the survival probability through a stochastic recurrence equation. The proposed models can effectively capture changing dependence over time and enhance both the in-sample and out-of-sample performance of integer-valued autoregressive models. This point is illustrated through an empirical application to a real-time series of crime reports. Additionally, this paper discusses the reliability of likelihood-based inference for the class of models. In particular, this study proves the consistency of the maximum likelihood estimator and a plug-in estimator for the conditional probability mass function in a misspecified model setting.