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October 2006 Efficient prediction for linear and nonlinear autoregressive models
Ursula U. Müller, Anton Schick, Wolfgang Wefelmeyer
Ann. Statist. 34(5): 2496-2533 (October 2006). DOI: 10.1214/009053606000000812


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.


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Ursula U. Müller. Anton Schick. Wolfgang Wefelmeyer. "Efficient prediction for linear and nonlinear autoregressive models." Ann. Statist. 34 (5) 2496 - 2533, October 2006.


Published: October 2006
First available in Project Euclid: 23 January 2007

zbMATH: 1106.62103
MathSciNet: MR2291508
Digital Object Identifier: 10.1214/009053606000000812

Primary: 62M20
Secondary: 62G05 , 62G20 , 62M05 , 62M10

Keywords: AR model , Donsker class , empirical likelihood , EXPAR model , functional central limit theorem , kernel smoothed empirical process , Owen estimator , plug-in-estimator , pseudo-observation , SETAR model , uniformly integrable bracketing entropy , uniformly integrable entropy , weighted density estimator

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 5 • October 2006
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