Statistical Inference for the Covariates-driven Binomial AR(1) Process

The binomial autoregressive (BAR(1)) process is very useful to model the integer-valued time series data defined on a finite range. It is commonly observed that the autoregressive coefficient is assumed to be a constant. To make the BAR(1) model more practical, this paper introduces a new random coefficient binomial autoregressive model, which is driven by covariates. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators of the model parameters are derived, and the asymptotic properties are obtained. The performance of these estimators is compared via a simulation study. An application to a real data example is also provided. The results show that the proposed model and methods perform well for the simulations and application.