Empirical likelihood for nonparametric regression functions under strong mixing high-frequency data

In this paper, we extend the empirical likelihood (EL) method and the adjusted EL method to nonparametric regression models with strong mixing high-frequency samples. We construct the block EL statistic and the adjusted EL statistic, respectively, for a nonparametric regression function and obtain their asymptotic properties under certain conditions. In addition, we conduct numerical simulations and an empirical analysis to show the performance of the confidence intervals for the nonparametric regression function based on the EL method, the adjusted EL method and the normal approximation (NA) method, which shows that the EL method performs better than the NA method and the adjusted EL method performs better than both the EL and NA methods.