A New Binomial AR(1) Process With Dependent Counting Series Driven by Explanatory Variables

ABSTRACT The paper proposes a novel binomial autoregressive process with generalized binomial thinning operator, meanwhile considering the effects of explanatory variables. The explanatory variables have effects on the autoregressive coefficients of this process, and we establish the relationship between them through logarithmic transformation, resulting in time‐varying autoregressive coefficients. The Bernoulli counting sequences in generalized binomial thinning operator are dependent. We deduce several essential properties of this process. The chosen estimation methods are classic conditional least squares and conditional maximum likelihood estimation. In addition, we test whether or not there are explanatory variables and then predicted based on the model. Eventually, we illustrate the applicability of this process by presenting numerical results and real data analysis.