Local Linear Quantile Regression for Time Series Under Near Epoch Dependence

Abstract

This paper aims to establish asymptotic normality of the local linear kernel estimator for quantile regression under near epoch dependence, a useful concept in characterising time series dependence of extensive interests in Econometrics. In particular, near epoch dependence can cover a wide range of linear or nonlinear time series models that are even not of strong or $\alpha$-mixing property (a property usually assumed in the nonlinear time series literature). Under the mild conditions, the Bahadur representation of the quantile regression estimators is established in weak convergence sense. The method provides much richer information than mean regression and covers much more processes, which do not satisfy general mixing conditions. Simulation and application to a real data set are studied, which demonstrate the usefulness of the introduced method for analysis of time series. The theoretical results of this paper will be of widely potential interest for time series econometric semiparametric quantile regression modelling.