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October 1999 Nonlinear wavelet estimation of time-varying autoregressive processes
Rainer Dahlhaus, Michael H. Neumann, Rainer Von Sachs
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Bernoulli 5(5): 873-906 (October 1999).

Abstract

We consider nonparametric estimation of the parameter functions ai(.), i = 1,...,p, of a time-varying autoregressive process. Choosing an orthonormal wavelet basis representation of the functions ai, the empirical wavelet coefficients are derived from the time series data as the solution of a least-squares minimization problem. In order to allow the ai to functions of inhomogeneous regularity, we apply nonlinear thresholding to the empirical coefficients and obtain locally smoothed estimates of the ai. We show that the resulting estimators attain the usual minimax L2 rates up to a logarithmic factor, simultaneously in a large scale of Besov classes. The finite-sample behaviour of our procedure is demonstrated by application to two typical simulated examples.

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Rainer Dahlhaus. Michael H. Neumann. Rainer Von Sachs. "Nonlinear wavelet estimation of time-varying autoregressive processes." Bernoulli 5 (5) 873 - 906, October 1999.

Information

Published: October 1999
First available in Project Euclid: 12 February 2007

zbMATH: 0954.62103
MathSciNet: MR1715443

Keywords: nonlinear thresholding , non-stationary processes , time series , time-varying autoregression , wavelet estimators

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability

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Vol.5 • No. 5 • October 1999
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