Bernoulli

  • Bernoulli
  • Volume 5, Number 5 (1999), 873-906.

Nonlinear wavelet estimation of time-varying autoregressive processes

Rainer Dahlhaus, Michael H. Neumann, and Rainer Von Sachs

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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.

Article information

Source
Bernoulli, Volume 5, Number 5 (1999), 873-906.

Dates
First available in Project Euclid: 12 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1171290403

Mathematical Reviews number (MathSciNet)
MR1715443

Zentralblatt MATH identifier
0954.62103

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

Citation

Dahlhaus, Rainer; Neumann, Michael H.; Von Sachs, Rainer. Nonlinear wavelet estimation of time-varying autoregressive processes. Bernoulli 5 (1999), no. 5, 873--906. https://projecteuclid.org/euclid.bj/1171290403


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