Spectral Density Estimation via Wavelet Shrinkage

We study the problem of estimating the spectral density of a stationary Gaussian time series. We use an orthogonal wavelet system whose members are periodic functions and have a nite number of non-zero Fourier coeecients { periodized Meyer wavelets. We apply shrinkage rules to the empirical wavelet coeecients. We show that estimates based on thresholds t j;n = j log n for certain j , with n the sample size, have near-optimal L 2 convergence rates, over any Besov class in a wide range. In some cases, which includes the Bump Algebra, wavelet shrinkage procedures signiicantly outperform classical linear procedures, such as window methods and AR approximation methods.