TY  - JOUR
Y1  - 2001///
PB  - Elsevier
AV  - public
A1  - Dahlhaus, Rainer
A1  - Neumann, Michael H.
CY  - Amsterdam
ID  - heidok20767
SP  - 277
VL  - 91
JF  - Stochastic Processes & Their Applications
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/20767/
EP  - 308
SN  - 0304-4149
TI  - Locally Adaptive Fitting of Semiparametric Models to Nonstationary Time Series
KW  - Locally stationary processes; Nonlinear thresholding; Nonparametric curve estimation;
Preperiodogram; Time series; Wavelet estimators
N2  - 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.
ER  -