Uniform convergence for Nadaraya-Watson estimators with non-stationary data

Nigel Chan and Qiying Wang

Abstract

This paper investigates the uniform convergence for the Nadaraya-Watson estimators in a non-linear cointegrating regression. Our results provide a optimal convergence rate without the compact set restriction, allowing for martingale innovation structure and the situation that the data regressor sequence is a partial sum of general linear process including fractionally integrated time series. We also investigate the uniform convergence for functionals of general non-stationary time series, which is of interests in its own right.

Keywords: Cointegration, uniform convergence, non-parametric regression, kernel estimation, nonstationarity, nonlinearity.

AMS Subject Classification: Primary 62G05;; secondary 62G20.