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 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.
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- Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
- Jan Beran & Yuanhua Feng, 2002. "Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 291-311, June.
- Beran, Jan & Ghosh, Sucharita & Sibbertsen, Philipp, 2000. "Nonparametric M-estimation with long-memory errors," Technical Reports 2000,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.