Repeated SPRT charts for monitoring INAR(1) processes

Poisson integer valued autoregressive (INAR) models have been proposed for modeling correlated count data. Poisson lognormal (PLN) INAR models extend their use to overdispersed contexts. In this paper, we will propose the use of a repeated Sequential Probability Ratio Test (SPRT) procedure to detect change in first‐order INAR and PLN INAR models. We consider change in the mean, the autocorrelation parameter, and the overdispersion parameter. Simulation results show the repeated SPRT procedure performs favorably relative to previously proposed CUSUM procedures that are based on either the observations themselves or residuals of the observations from predicted values. A dataset on invasive insect species is used to illustrate the repeated SPRT procedure.