The use of wavelets for spectral density estimation with local bandwidth adaptation

We consider the problem of estimating the spectral density of a discrete-time, wide-sense stationary, real, Gaussian random process from a set of 2N observations. Consistent estimates may be obtained by suitable processing of the empirical spectral density estimates (periodogram). Wavelet techniques can be used for combining information about the spectral density at different resolutions. We present an estimation technique based on the following two paradigms: large-sample model for the data; and inference on the wavelet coefficients of the log spectral density