On robust local polynomial estimation with long-memory errors

Abstract

Prediction in time series models with a trend requires reliable estimation 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-estimation is considered for the case where the error process exhibits long-range dependence. In contrast to the iid case, all M-estimators are asymptotically equivalent to the least-square solution, under the (ideal) Gaussian model. The potential usefulness of the proposal for forecasting is illustrated by practical and simulated examples. A simulation study shows that outliers have a major effect on nonrobust bandwidth selection, in particular due to the change of the dependence structure.