Nonparametric Inference for Time-varying Coefficient Quantile Regression

The paper considers nonparametric inference for quantile regression models with time-varying coefficients. The errors and covariates of the regression are assumed to belong to a general class of locally stationary processes and are allowed to be cross-correlated. Simultaneous confidence tubes (SCT) and integrated squared difference tests (ISDT) are proposed for simultaneous nonparametric inference of the latter models with asymptotically correct coverage probabilities and type I error rates. Our methodologies are shown to possess certain asymptotically optimal properties. Furthermore, we propose an information criterion which performs consistent model selection for nonparametric quantile regression models of non-stationary time series. For implementation, a wild bootstrap procedure is proposed which is shown to be robust to the dependent and non-stationary data structure. Our method is applied to studying the asymmetric and time-varying dynamic structures of the US unemployment rate since the 1940s.