Empirical Likelihood Confidence Intervals for Nonparametric Nonlinear Nonstationary Regression Models

By using the empirical likelihood (EL), we consider the construction of pointwise confidence intervals (CIs) for nonparametric nonlinear nonstationary regression models with nonlinear nonstationary heterogeneous errors. It is well known that the EL-based CI has attractive properties such as data dependency and automatic studentization in cross-sectional and weak-dependence models. We extend EL theory to the nonparametric nonlinear nonstationary regression model and show that the log-EL ratio converges to a chi-squared random variable with one degree of freedom. This means that Wilks' theorem holds even if the covariate follows a nonstationary process. We also conduct empirical analysis of Japan's inverse money demand to demonstrate the data-dependency property of the EL-based CI.