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Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes

  • We consider nonparametric estimation of the coefficients a_i(.), i=1,...,p, on a time-varying autoregressive process. Choosing an orthonormal wavelet basis representation of the functions a_i(.), 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 a_i(.) to be functions of inhomogeneous regularity, we apply nonlinear thresholding to the empirical coefficients and obtain locally smoothed estimates of the a_i(.). We show that the resulting estimators attain the usual minimax L_2-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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Author:Michael H. Neumann, Rainer von Sachs, R. Dahlhaus
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5468
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (145)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Nonstationary processes; nonlinear thresholding; time series; time-varying autoregression; wavelet estimators
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):62-XX STATISTICS / 62Fxx Parametric inference / 62F10 Point estimation
62-XX STATISTICS / 62Mxx Inference from stochastic processes / 62M10 Time series, auto-correlation, regression, etc. [See also 91B84]
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011