Plug-in bandwidth selector for local polynomial regression estimator with correlated errors

Abstract

Consider the fixed regression model where the error random variables are coming from a strictly stationary, non-white noise stochastic process. In a situation like this, automated bandwidth selection methods for non-parametric regression break down. We present a plug-in method for choosing the smoothing parameter for local least squares estimators of the regression function. The method takes the presence of correlated errors explicitly into account through a parametric correlation function specification. The theoretical performance for the local linear estimator of the regression function is obtained in the case of an AR(1) correlation function. These results can readily be extended to other settings, such as different parametric specifications of the correlation function, derivative estimation and multiple non-parametric regression. Estimators of regression functionals and the error correlation based on local least squares ideas are developed in this article. A simulation study and an analysis with real economic data illustrate the selection method proposed.