ON ADAPTIVE ESTIMATION FOR LOCALLY STATIONARY WAVELET PROCESSES AND ITS APPLICATIONS
Sébastien Van Bellegem, Rainer von Sachs · International Journal of Wavelets Multiresolution and Information Processing · 2004
The class of locally stationary wavelet processes is a wavelet-based model for covariance nonstationary zero mean time series. This paper presents an algorithm for the pointwise adaptive estimation of their time-varying spectral density. The performance of the procedure is evaluated on simulated and real time series. Two applications of the procedure are also presented and evaluated on real data. The first is a test of local existence for the coefficients of the so-called wavelet periodogram. The second is a new test of covariance stationarity.