Weighted Local Nonparametric Regression with Dependent Errors: Study of Real Private Residential Fixed Investment in the USA

Abstract

This paper presents an overview of the existing literature on the nonparametric local polynomial (LPR) estimator of the regression function and its derivatives when the observations are dependent. When the errors of the regression model are correlated and follow an ARMA process, Vilar-Fernández and Francisco-Fernández (2002) proposed a modification of the LPR estimator, called the generalized local polynomial (GLPR) estimator, based on, first, transforming the regression model to get uncorrelated errors and then applying the LPR estimator to the new model. Some of the most significant asymptotic properties of these two weighted local estimators, including some guidelines on how to select the bandwidth parameter, are reviewed. Finally, these techniques are used to study the real private residential fixed investment in the USA.