Estimation for time-varying coefficient smoothed quantile regression

Time-varying coefficient regression is commonly used in the modeling of nonstationary stochastic processes. In this paper, we consider a time-varying coefficient <b>con</b>volution-type smoothed <b>qu</b>antil<b>e</b> <b>r</b>egression (<i>conquer</i>). The covariates and errors are assumed to belong to a general class of locally stationary processes. We propose a local linear <i>conquer</i> estimator for the varying-coefficient function, and obtain the global Bahadur-Kiefer representation, which yields the asymptotic normality. Furthermore, statistical inference on simultaneous confidence bands is also studied. We investigate the finite-sample performance of the <i>conquer</i> estimator and confirm the validity of our asymptotic theory by conducting extensive simulation studies. We also consider financial volatility data as an example of a real-world application.