Statistical inferences in quantile regression models with autoregressive errors

Quantile regression is widely used in practice because it can comprehensively describe the relationship between response and covariates. However, it is known that conventional quantile regression estimators may be biased when the model errors are correlated, which motivates us to consider the current setting in which the model errors follow an autoregressive process. An iterative procedure is developed to estimate the unknown parameters. We show the asymptotic normality of the resulting estimators under mild conditions. A random weighted bootstrap-based test statistic is also suggested by the complex structure of the asymptotic covariance matrix. Simulation studies and a real data example are conducted to illustrate the finite sample performance of the developed methods.