On robust local polynomial estimation with long-memory errors

Prediction in time series models with a trend requires reliable estima- tion of the trend function at the right end of the observed series. Local polynomial smoothing is a suitable tool because boundary corrections are included implicitly. However, outliers may lead to unreliable estimates, if least squares regression is used. In this paper, local polynomial smoothing based on M-estimators are asymptotically equivalent to the least square solution, under the (ideal) Gaussian model. Outliers turn out to have a major effect on nonrobust bandwidht selection, in particular due to the change of the dependence structure.