Wavelet smoothing of evolutionary spectra by non-linear thresholding

We consider wavelet estimation of the time-dependent (evolutionary) power spectrum of a locally stationary time series in a model which was recently introduced by Dahlhaus. Allowing for departures from stationarity proves useful for modelling, e.g., transient phenomena, quasi-oscillating behavior or spectrum modulation. In contrast to classical parametric and nonparametric (linear) approaches we use nonlinear thresholding of the empirical wavelet coefficients of the evolutionary spectrum. We show how these techniques allow for both adaptively reconstructing the local structure in the time-frequency plane and for denoising the resulting estimates. To this end a threshold choice is derived which is motivated by minimax properties w.r.t. the integrated mean squared error. Our approach is based on a 2-d orthogonal wavelet transform modified by using a cardinal Lagrange interpolation function on the finest scale. As an example, we apply our procedure to a time-varying spectrum motivated from mobile radio propagation. (orig.)SIGLEAvailable from TIB Hannover: RO 5810(106)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman