Robust Inference for Time Series Quantile Regression: A Dependent Wild Bootstrap-Based Approach

Quantile regression is widely used to study heterogeneous effects, but inference in time series settings remains challenging when regression errors are serially correlated. Building on the dependent wild bootstrap, we develop an inference procedure for linear time series quantile regression that reweights the restricted quantile score with tapered multipliers and employs a one-step bootstrap update together with the HAC-based studentization. The procedure avoids repeated solution of a non-smooth quantile regression problem within each bootstrap draw while targeting the same inferential object as robust HAC testing. Under strong mixing and standard smoothness and bandwidth conditions, we establish asymptotic validity of the bootstrap test and derive its local power under Pitman alternatives. Monte Carlo results indicate improved size control relative to conventional and robust HAC methods, especially under strong dependence, with only modest differences in power. An application to the determinants of U.S. housing prices over the past four decades illustrates the practical usefulness of the method.