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.
Author: | Michael H. Neumann, Rainer von Sachs, R. Dahlhaus |
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URN: | urn:nbn:de:hbz:386-kluedo-5468 |
Series (Serial Number): | Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (145) |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 1999 |
Year of first Publication: | 1999 |
Publishing Institution: | 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: | Kaiserslautern - 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 |