Haar-Fisz estimation of evolutionary wavelet spec- tra

We propose a new “Haar-Fisz” technique for estimating the time-varying, piecewise constant local variance of a locally stationary Gaussian time series. We apply our technique to the estimation of the spectral structure in the Locally Stationary Wavelet model. Our method combines Haar wavelets and the variance stabilizing Fisz transform. The resulting estimator is mean-square consistent, rapidly computable, easy to implement, and performs well in practice. We also introduce the “Haar-Fisz transform”, a device for stabilizing the variance of scaled chi-square data and bringing their distribution close to Gaussianity.