Regression Quantiles for Time Series

In this article we study nonparametric estimation of regression quantiles by inverting a weighted Nadaraya-Watson estimator (WNW) of conditional distribution function, which was rst used by Hall, Woll and Yao (1999). First, under some regularity conditions, we establish the asymptotic normality and weak consistency of the WNW conditional distribution estimator for-mixing time series at both boundary and interior points, and we show that the WNW conditional distribution estimator not only preserves the bias, variance, and more importantly, automatic good boundary behavior properties of local linear \double-kernel" estimators introduced by Yu and Jones (1998), but also has the additional advantage of always being a distribution itself. Secondly, it is shown that under some regularity conditions, the WNW conditional quantile estimator is weekly consistent and normally distributed and that it inherits all good properties from the WNW conditional distribution estimator. A simulation study is carried out to illustrate the performance of the estimates and a real example is also used to demonstrate the methodology.