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Haar-Fisz estimation of evolutionary wavelet spectra

By Piotr Fryzlewicz and Guy P. Nason

Abstract

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 scaled χ2-data and bringing their distribution close to Gaussianity

Topics: HA Statistics
Publisher: Wiley on behalf of the Royal Statistical Society
Year: 2006
DOI identifier: 10.1111/j.1467-9868.2006.00558.x
OAI identifier: oai:eprints.lse.ac.uk:25227
Provided by: LSE Research Online
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