On robust local polynomial estimation with long-memory errors

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, (C) 2002 International Institute of Forecasters. Published by Elsevier Science B.V. All rights reserved.