eprintid: 21429
rev_number: 15
eprint_status: archive
userid: 2326
dir: disk0/00/02/14/29
datestamp: 2016-07-01 07:47:06
lastmod: 2016-08-01 12:04:03
status_changed: 2016-07-01 07:47:06
type: article
metadata_visibility: show
creators_name: Dahlhaus, Rainer
creators_name: Neumann, Michael H.
creators_name: von Sachs, Rainer
title: Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes
subjects: ddc-510
divisions: i-110400
keywords: Nonlinear thresholding; non-stationary processes; time series; time-varying autoregression;
wavelet estimators
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.
date: 1999
id_scheme: DOI
id_number: 10.11588/heidok.00021429
schriftenreihe_cluster_id: sr-10b
schriftenreihe_order: 09
ppn_swb: 1657883949
own_urn: urn:nbn:de:bsz:16-heidok-214291
language: eng
bibsort: DAHLHAUSRANONLINEARW1999
full_text_status: public
publication: Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability
volume: 5
number: 5
place_of_pub: Aarhus
pagerange: 873-906
issn: 1350-7265
citation:   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     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/21429/1/report.09.pdf