Conference Agenda

Integer-valued autoregressive (INAR) models provide a flexible framework for modeling count time series through thinning operators that emulate autoregressive dynamics while respecting the discrete nature of the data. These models naturally accommodate both equidispersion and overdispersion, features commonly observed in count-valued processes.

This paper investigates INAR models with structural breaks, with particular emphasis on the detection and estimation of parameter changes over time—an issue of critical importance in dynamic settings such as epidemics, policy interventions, and other regime-shifting phenomena. We consider both classical and Bayesian inferential approaches for identifying change points and estimating model parameters.

The classical framework is based on maximum likelihood estimation, where structural changes are detected using a CUSUM-based procedure, followed by a focused grid search within a window centered around the candidate breakpoint. The Bayesian approach employs advanced Markov Chain Monte Carlo (MCMC) techniques, incorporating hidden Markov chains to model latent regimes and infer structural shifts probabilistically.

A comprehensive simulation study is conducted under a variety of scenarios, including differing regime lengths and sample size proportions, and distributional characteristics. Finally, the proposed methodologies are illustrated through an application to real-world health indicator data, demonstrating their practical effectiveness in capturing complex dynamics and structural changes in count time series.