Empirical likelihood for partially time-varying coefficient models with dependent observations

In this paper, we apply the empirical likelihood method to study the partially time-varying coefficient models with a random design and a fixed design under dependent assumptions. A nonparametric version of Wilks’ theorem is derived for the fixed-design case. For the random-design case, it is proved that the empirical log-likelihood ratio of the regression parameters admits a limiting distribution with a weighted sum of independent chi-squared distributions. In order that Wilks’ phenomenon holds, we propose an adjusted empirical log-likelihood (ADEL) ratio for the regression parameters. The ADEL is shown to have a standard chi-squared limiting distribution. Simulation studies are undertaken to indicate that the proposed methods work better than the normal approximation-based approach.