Haar–Fisz estimation of evolutionary wavelet spectra

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2006 · Volume 68 · Issue 4

DOI: 10.1111/j.1467-9868.2006.00558.x

Abstract

Summary.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 and easy to implement, and performs well in practice. We also introduce the ‘Haar–Fisz transform’, a device for stabilizing the variance of scaledχ2-data and bringing their distribution close to Gaussianity.

Keywords

Heteroscedasticity, Log-transform, Thresholding estimators, Wavelet periodogram, Wavelet spectrum

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