The Empirical Likelihood for First-Order Random Coefficient Integer-Valued Autoregressive Processes

This article studies the empirical likelihood method for the first-order random coefficient integer-valued autoregressive process. The limiting distribution of the log empirical likelihood ratio statistic is established. Confidence region for the parameter of interest and its coverage probabilities are given, and hypothesis testing is considered. The maximum empirical likelihood estimator for the parameter is derived and its asymptotic properties are established. The performances of the estimator are compared with the conditional least squares estimator via simulation.