title: Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes
creator: Dahlhaus, Rainer
creator: Neumann, Michael H.
creator: von Sachs, Rainer
subject: ddc-510
subject: 510 Mathematics
description: 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.
date: 1999
type: Article
type: info:eu-repo/semantics/article
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/21429/1/report.09.pdf
identifier: DOI:10.11588/heidok.00021429
identifier: urn:nbn:de:bsz:16-heidok-214291
identifier:   Dahlhaus, Rainer ; Neumann, Michael H. ; von Sachs, Rainer  (1999) Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes.  Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability, 5 (5).  pp. 873-906.  ISSN 1350-7265     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/21429/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng