Chain binomial models and binomial autoregressive processes

Summary We establish a connection between a class of chain‐binomial models of use in ecology and epidemiology and binomial autoregressive (AR) processes. New results are obtained for the latter, including expressions for the lag‐ conditional distribution and related quantities. We focus on two types of chain‐binomial model, extinction–colonization and colonization–extinction models, and present two approaches to parameter estimation. The asymptotic distributions of the resulting estimators are studied, as well as their finite‐sample performance, and we give an application to real data. A connection is made with standard AR models, which also has implications for parameter estimation.