In this paper, we investigate empirical likelihood inference for both the regression parameter and the coefficient function in partially linear functional-coefficient autoregressive errors-in-variables models. It is assumed that the observations form a stationary \(\alpha \) -mixing sequence. We propose a bias-corrected local linear estimator for the coefficient function, along with an estimated empirical likelihood (EEL) for the regression parameter. The dependence of observations complicates the limiting distribution of the EEL, which is shown to be a mixture of central chi-squared distributions. To recover Wilks’ phenomenon, we further develop an adjusted empirical likelihood (AEL) method that requires only standard chi-square tables. Additionally, we derive the maximum empirical likelihood estimator (MELE) for the regression parameter and establish its asymptotic normality. Based on the MELE, we construct an empirical likelihood for the coefficient function, and the resulting statistic asymptotically follows a chi-squared distribution. Simulation studies and real data applications are conducted to assess the finite-sample performance of the proposed methods.
