eprintid: 20767
rev_number: 14
eprint_status: archive
userid: 2326
dir: disk0/00/02/07/67
datestamp: 2016-05-25 12:59:45
lastmod: 2016-05-30 09:01:46
status_changed: 2016-05-25 12:59:45
type: article
metadata_visibility: show
creators_name: Dahlhaus, Rainer
creators_name: Neumann, Michael H.
title: Locally Adaptive Fitting of Semiparametric Models to Nonstationary Time Series
subjects: ddc-510
divisions: i-110400
keywords: Locally stationary processes; Nonlinear thresholding; Nonparametric curve estimation;
Preperiodogram; Time series; Wavelet estimators
abstract: We fit a class of semiparametric models to a nonstationary process. This class is parametrized by a mean function µ( · ) and a p-dimensional function theta ( · ) = (theta(1)( · ) , ..., theta(p) ( · ))´ that parametrizes the time-varying spectral density ftheta( · ) (lambda). Whereas the mean function is estimated by a usual kernel estimator, each component of theta ( · ) is estimated by a nonlinear wavelet method. According to a truncated wavelet series expansion of theta(i) ( · ), we define empirical versions of the corresponding wavelet coefficients by minimizing an empirical version of the Kullback-Leibler distance. In the main smoothing step, we perform nonlinear thresholding on these coefficients, which finally provides a locally adaptive estimator of theta(i) ( · ). This method is fully automatic and adapts to different smoothness classes. It is shown that usual rates of convergence in Besov smoothness classes are attained up to a logarithmic factor.
date: 2001
publisher: Elsevier
id_scheme: DOI
id_number: 10.11588/heidok.00020767
schriftenreihe_cluster_id: sr-10a
schriftenreihe_order: 60
ppn_swb: 1656797771
own_urn: urn:nbn:de:bsz:16-heidok-207676
language: eng
bibsort: DAHLHAUSRALOCALLYADA2001
full_text_status: public
publication: Stochastic Processes & Their Applications
volume: 91
place_of_pub: Amsterdam
pagerange: 277-308
issn: 0304-4149
citation:   Dahlhaus, Rainer ; Neumann, Michael H.  (2001) Locally Adaptive Fitting of Semiparametric Models to Nonstationary Time Series.  Stochastic Processes & Their Applications, 91.  pp. 277-308.  ISSN 0304-4149     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/20767/1/beitrag.60.pdf