Locally adaptive fitting of semiparametric models to nonstationary time series

Rainer Dahlhaus () and Michael H. Neumann

Stochastic Processes and their Applications, 2001, vol. 91, issue 2, 277-308

Abstract: We fit a class of semiparametric models to a nonstationary process. This class is parametrized by a mean function [mu](·) and a p-dimensional function [theta](·)=([theta](1)(·),...,[theta](p)(·))' that parametrizes the time-varying spectral density f[theta](·)([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.

Keywords: Locally; stationary; processes; Nonlinear; thresholding; Nonparametric; curve; estimation; Preperiodogram; Time; series; Wavelet; estimators (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (7)

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