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Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes

Dahlhaus, Rainer ; Neumann, Michael H. ; von Sachs, Rainer

In: Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability, 5 (1999), Nr. 5. pp. 873-906. ISSN 1350-7265

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Abstract

We consider nonparametric estimation of the coefficients, of atime-varying autoregressive process. Choosing an orthonormal wavelet basisrepresentation of the coefficient functions, the empirical wavelet coefficientsare derived from the time series data as the solution of a least squares minimizationproblem. In order to allow the coefficient functions to be of inhomogeneous regularity,we apply nonlinear thresholding to the empirical coefficients and obtain locally smoothedestimates of the coefficient functions. We show that the resulting estimators attain theusual minimax L_2-rates up to a logarithm factor, simultaneously in a large scale of Besovclasses.

Item Type: Article
Journal or Publication Title: Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability
Volume: 5
Number: 5
Place of Publication: Aarhus
Date Deposited: 01 Jul 2016 07:47
Date: 1999
ISSN: 1350-7265
Page Range: pp. 873-906
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Uncontrolled Keywords: Nonlinear thresholding; non-stationary processes; time series; time-varying autoregression; wavelet estimators
Schriftenreihe ID: Beiträge zur Statistik > Reports
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