Quantile Inference for Near-integrated Autoregressive Time Series with Infinite Variance

The limiting distribution of the quantile estimate for the autoregressive coefficient of a near-integrated first order autoregressive model with infinite variance errors is derived. Since the limiting distribution depends on the unknown density function of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the near unit root model without knowing the density function. Numerical simulations are conducted to compare the performance of the empirical likelihood method and the least squares procedure. It is found that the empirical likelihood method outperforms the least squares procedure in general.