Self-exciting hysteretic binomial autoregressive processes

This paper introduces an observation-driven integer-valued time series model, in which the underlying generating stochastic process is binomially distributed conditional on past information in the form of a hysteretic autoregressive structure. The basic probabilistic and statistical properties of the model are discussed. Conditional least squares, weighted conditional least squares, and maximum likelihood estimators are obtained together with their asymptotic properties. A search algorithm for the two boundary parameters, and the corresponding strong consistency of the estimators, are also provided. Finally, some numerical results on the estimators and a real-data example are presented.