Improved local polynomial estimation in nonparametric time series regression

We propose a modification of local polynomial time series fitting which improves the efficiency of the conventional method when the observation error is strongly mixing. This generalizes the work of Xiao et. al. in 2003, who considered an error process with an invertible linear representation. Here, we do not suppose a certain functional structure on the random observation error. Furthermore, we allow for heteroscedasticity. The procedure is based on a pre-whitening transformation of the data. The dependent variable as well as the unknown variance function are estimated via preliminary local polynomial regression. Establishing its asymptotic distribution, we show that the proposed estimator is more efficient than the conventional one. In a simulation study, the performance of our estimator on finite samples is investigated