Efficient prediction for linear and nonlinear autoregressive models
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The Annals of Statistics

Efficient prediction for linear and nonlinear autoregressive models

Ursula U. Müller, Anton Schick, and Wolfgang Wefelmeyer

Source: Ann. Statist. Volume 34, Number 5 (2006), 2496-2533.

Abstract

Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear autoregressive models driven by independent innovations, appropriate smoothed and weighted von Mises statistics of residuals estimate conditional expectations at better parametric rates and are asymptotically efficient. The proof is based on a uniform stochastic expansion for smoothed and weighted von Mises processes of residuals. We consider, in particular, estimation of conditional distribution functions and of conditional quantile functions.

Primary Subjects: 62M20
Secondary Subjects: 62G05, 62G20, 62M05, 62M10
Keywords: Empirical likelihood; Owen estimator; weighted density estimator; kernel smoothed empirical process; functional central limit theorem; Donsker class; uniformly integrable entropy; uniformly integrable bracketing entropy; pseudo-observation; plug-in-estimator; AR model; EXPAR model; SETAR model

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Permanent link to this document: http://projecteuclid.org/euclid.aos/1169571805
Digital Object Identifier: doi:10.1214/009053606000000812

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