More efficient estmation in nonparametric regression with nonparametric autocorrelated errors

We define a three-step procedure for more efficient estimation of the nonparametric regression mean with nonparametric autocorrelated errors. The procedure is based upon a nonparametric prewhitening transformation of the dependent variable that has to be estimated from the data by a local polynomial technique. We establish the asymptotic distribution of our estimator under weak dependence conditions and show that it is more efficient than the conventional local polynomial estimator. Furthermore, we consider criterion functions based on the linear exponential family, which include the local polynomial least squares criterion as a special case. Simulation evidence suggests that significant gains can be achieved in finite samples with our approach.