On recursive estimation for time varying autoregressive processes
Eric Moulines, Pierre Priouret, and François Roueff
Source: Ann. Statist. Volume 33, Number 6 (2005), 2610-2654.
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.
Primary Subjects: 62M10, 62G08, 60J27
Secondary Subjects: 62G20
Keywords: Locally stationary processes; nonparametric estimation; recursive estimation; time-varying autoregressive model
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1140191668
Digital Object Identifier: doi:10.1214/009053605000000624
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