Empirical likelihood inference for INAR(1) model with explanatory variables

The integer autoregressive (INAR) model defined through the thinning operator can be used to model many count data in applications. Usually, the autoregressive parameter in the thinning operator is assumed to be constant or random variable varying in [0,1]. To make the INAR model more practical, in this paper we consider the INAR(1) model with explanatory variables incorporated into the autoregressive parameter. We use the empirical likelihood method to investigate this model. The empirical likelihood ratio statistic is derived and its asymptotic distribution is shown to be a chi-squared distribution. The maximum empirical likelihood estimator for the parameters is also given and its asymptotic properties are established. Simulation study is conducted for the evaluation of the developed approach and an application to a real data example is provided.