Functional-coefficient quantile regression with nonstationary time series

Han-Ying Liang, Yu Shen and Qiying Wang

Abstract

This paper explores kernel and local linear quantile estimation for a functional-coefficient regression model with nonstationary time series as regressor. Our main results are established by allowing for the heavy-tailed distributional assumption in the error term, which enables the quantile approach applicable in econometrics and many other fields where outliers and aberrant observations are at present. Our main results further indicate that the linear term in kernel quantile estimator can not be eliminated from the asymptotic bias. This feature is different from the previous researches on nonlinear regression with nonstationary time series, where the conventional kernel estimator is shown to have the same limit distribution (to the second order including bias) as the local linear nonparametric estimator. Simulation result shows good performance for the proposed estimators as predicted by our asymptotic theory. An empirical application for the monthly road casualties in Great Britain has also been considered.

Keywords: Functional-coefficient regression, Kernel quantile smoothing, local linear quantile smoothing, nonstationary time series.