Empirical Likelihood Statistical Inference for the BINAR(1) Process

In this paper, we apply the empirical likelihood (EL) approach to the bivariate first-order integer-valued autoregressive (BINAR(1)) model. The maximum empirical likelihood (MEL) estimator for this process is constructed by the empirical likelihood ratio (ELR) statistic derived from the EL method. We then discuss the asymptotic properties of this estimator. Subsequently, the model parameters are estimated using the MEL method, the conditional least squares method, and the conditional maximum likelihood method. The finite-sample performance of the proposed estimation procedures is examined through Monte Carlo simulation experiments. A real data example is further presented.