Empirical likelihood inference in autoregressive models with time-varying variances

This paper develops the empirical likelihood ( $ \mathrm {EL} $ EL) 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 $ \mathrm {EL} $ EL 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.