Abstract

Time series of counts are prevalent in various scientific fields, such as tracking the daily number of hospital admissions, minute-by-minute stock transactions, or the monthly count of car accidents in a specific region. A notable model for stationary count series, derived from the work of Steutel & Van Harn (1979), uses a thinning operation within a difference equation scheme. This approach mimics the autoregressive moving-average method to generate stationary integer-valued series with negative binomial, geometric, and Poisson marginal distributions. Among the most studied models is the integer autoregressive model, known as INAR(p), where p represents the autoregressive order. These models typically assume constant parameters over time, an assumption that may not hold in practice. For example, during an epidemic, the daily count of affected cases usually starts low, increases, and eventually decreases. Detecting breakpoints in count processes is crucial for both methodological and practical reasons, such as validating scientific hypotheses, monitoring safety-critical processes, and validating modeling assumptions. Considering the INAR model with structural breaks and an innovation process that incorporates overdispersion, we apply the methodology proposed by Kashikar et al. (2014). This approach identifies breakpoints, estimates parameters, and predicts future observations using an MCMC scheme. Additionally, predictive methods are addressed to facilitate model choice and model checking. The proposed methodology is applied to a real dataset in the context of health indicators. Different methods for detecting single or multiple change points are compared, covering both frequentist and Bayesian approaches