Empirical likelihood for linear and log-linear INGARCH models

The integer-valued GARCH model is a popular tool for modeling time series of counts. This paper develops empirical likelihood methods for the linear and log-linear integer-valued GARCH models, respectively. We consider three aspects of the empirical likelihood method: estimates, confidence regions and test. For both models, an empirical log-likelihood ratio statistic is derived and its asymptotic distribution is shown to be a chi-squared distribution. Simulation studies lead to superior performance of the empirical likelihood method compared with the conventional treatments in the literature. An application to a real data example is also provided.