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 convolution-type smoothed quantile regression (conquer). The covariates and errors are assumed to belong to a general class of locally stationary processes. We propose a local linear conquer 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 conquer 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.