Spurious regression in nonparametric models

Abstract

This paper develops the asymptotic theory for the Nadaraya-Watson kernel estimator and local polynomial estimator when two independently integrated processes are used in a nonlinear regression. It is shown that the Nadaraya-Watson kernel estimator and the local polynomial estimator do not possess limiting distributions in this context but actually diverge at rate n1/2 as the sample size n→∞, and this is slower than that of parameters in linear regression. In spite of the difference in the rate of divergence between the parametric and nonparametric cases, they all can induce spurious regression.