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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

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.

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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. https://doi.org/10.1214/009053606000000812

Information

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

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

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

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 5 • October 2006
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