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December 2005 On recursive estimation for time varying autoregressive processes
Eric Moulines, Pierre Priouret, François Roueff
Ann. Statist. 33(6): 2610-2654 (December 2005). DOI: 10.1214/009053605000000624

Abstract

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong to appropriate smoothness classes. An adequate normalization for the correction term used in the recursive estimation procedure allows for very mild assumptions on the innovations distributions. The rate of convergence of the pointwise estimates is shown to be minimax in β-Lipschitz classes for 0<β≤1. For 1<β≤2, this property no longer holds. This can be seen by using an asymptotic expansion of the estimation error. A bias reduction method is then proposed for recovering the minimax rate.

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Eric Moulines. Pierre Priouret. François Roueff. "On recursive estimation for time varying autoregressive processes." Ann. Statist. 33 (6) 2610 - 2654, December 2005. https://doi.org/10.1214/009053605000000624

Information

Published: December 2005
First available in Project Euclid: 17 February 2006

zbMATH: 1084.62089
MathSciNet: MR2253097
Digital Object Identifier: 10.1214/009053605000000624

Subjects:
Primary: 60J27 , 62G08 , 62M10
Secondary: 62G20

Keywords: Locally stationary processes , nonparametric estimation , recursive estimation , time-varying autoregressive model

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 6 • December 2005
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