Issues on quantile autoregression ∗

We congratulate Koenker and Xiao on their interesting and important contribution to the quantile autoregression (QAR). The paper provides a comprehensive overview on the QAR model, from probabilistic aspects, to model identification, statistical inferences, and empirical applications. The attempt to integrate the quantile regression and the QAR process is intriguing. It demonstrates surprisingly that nonparametric coefficient functions can be estimated at root-n rate for the QAR processes. The authors then put forward some useful tools for testing significance of lag-variables and asymmetric dynamics of the time series. We appreciate the opportunity to comment several aspects of this article.