2004), Unit root quantile autoregression inference

Abstract. We study statistical inference in quantile autoregression models when the largest au-toregressive coecient may be unity. The limiting distribution of a quantile autoregression estima-tor and its t-statistic is derived. The asymptotic distribution is not the conventional Dickey-Fuller distribution, but a linear combination of the Dickey-Fuller distribution and the standard normal, with the weight determined by the correlation coecient of related time series. Inference methods based on the estimator are investigated asymptotically. Monte Carlo results indicate that the new inference procedures have power gains over the conventional least squares based unit root tests in the presence of non-Gaussian disturbances. An empirical application of the model to US macroeconomic time series data further illustrates the potential of the new approach. 1