Nonparametric Wavelet Methods for Nonstationary Time Series

This article gives an overview on nonparametric modelling of nonstationary time series and estimation of their time-changing spectral content by modern denoising (smoothing) methods. For the modelling aspect localized decompositions such as various local Fourier (spectral) representations are discussed, among which wavelet and local cosine bases are most prominent ones. For the estimation of the possibly time-varying coeecients of these local representations wavelet denoising algorithms are applied and their particular properties in the context of time{ frequency and time{scale analysis is discussed. In particular non{linear wavelet thresholding, including recent developments of generalizing its usefulness for non{identically, correlated and even non{stationary noise, is brieey reviewed as this is the unifying component of the estimation algorithms. The introduced procedures are illustrated by application to various simulated and real data examples from time{frequency and time{scale analysis, respectively.