Empirical likelihood inference in autoregressive models with time-varying variances

This paper develops the empirical likelihood ( ) inference procedure for parameters in autoregressive models with the error variances scaled by an unknown nonparametric time-varying function. Compared with existing methods based on non-parametric and semi-parametric estimation, the proposed test statistic avoids estimating the variance function, while maintaining the asymptotic chi-square distribution under the null. Simulation studies demonstrate that the proposed procedure (a) is more stable, i.e., depending less on the change points in the error variances, and (b) gets closer to the desired confidence level, than the traditional test statistic.