Haar-Fisz estimation of evolutionary wavelet spectra

PZ Fryzlewicz, GP Nason

Research output: Contribution to journalArticle (Academic Journal)

42 Citations (Scopus)

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 chi(2)-data and bringing their distribution close to Gaussianity.
Translated title of the contributionHaar-Fisz estimation of evolutionary wavelet spectra
Original languageEnglish
Pages (from-to)611 - 634
Number of pages24
JournalJournal of the Royal Statistical Society Series B - Statistical Methodology
Volume68 (4)
DOIs
Publication statusPublished - Sep 2006

Bibliographical note

Publisher: Blackwell Publishing
Other identifier: IDS number 076AD

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