On robust local polynominal estimation with long-memory errors - Jan Beran; Yuanhua Feng; Sucharita Ghosh; Philipp Sibbertsen (Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2000)
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 constrast to the iid case, all 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 bandwidth selection, in particular due to the change of the dependence structure.
Keywords: 519; Zeitreihenanalyse; Nichtparametrisches Verfahren; Robustes Verfahren; Theorie; Statistischer Fehler