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Locally Adaptive Fitting of Semiparametric Models to Nonstationary Time Series

Dahlhaus, Rainer ; Neumann, Michael H.

In: Stochastic Processes & Their Applications, 91 (2001), pp. 277-308. ISSN 0304-4149

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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.

Item Type: Article
Journal or Publication Title: Stochastic Processes & Their Applications
Volume: 91
Publisher: Elsevier
Place of Publication: Amsterdam
Date Deposited: 25 May 2016 12:59
Date: 2001
ISSN: 0304-4149
Page Range: pp. 277-308
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Uncontrolled Keywords: Locally stationary processes; Nonlinear thresholding; Nonparametric curve estimation; Preperiodogram; Time series; Wavelet estimators
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
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