title: Locally Adaptive Fitting of Semiparametric Models to Nonstationary Time Series
creator: Dahlhaus, Rainer
creator: Neumann, Michael H.
subject: ddc-510
subject: 510 Mathematics
description: 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.
publisher: Elsevier
date: 2001
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/20767/1/beitrag.60.pdf
identifier: DOI:10.11588/heidok.00020767
identifier: urn:nbn:de:bsz:16-heidok-207676
identifier:   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     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/20767/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng