Robust estimators under a semiparametric partly linear autoregression model: Asymptotic behavior and bandwidth selection

BIANCO, ANA; BOENTE, GRACIELA

JOURNAL OF TIME SERIES ANALYSIS

Blackwell Publishing

Año: 2007 vol. 28 p. 274 - 306

0143-9782

In this paper, under a semiparametric partly linear autoregression model, a family of robust estimates for the autoregression parameter and the autoregression function is studied. The proposed estimates are based on a three step procedure, in which regression robust estimates and robust smoothing techniques are combined. Asymptotic results on the autoregression estimates are derived. Besides, combining robust procedures with M--smoothers, predicted values for the series and detection residuals, which allow to detect anomalous data, are introduced. Robust cross--validation methods to select the smoothing parameter are presented as an alternative to the classical ones, which are sensitive to outlying observations. A Monte Carlo study is conducted in order to compare the performance of the proposed criteria. Finally, the asymptotic distribution of the autoregression parameter estimate is stated uniformly over the smoothing parameter.