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Haar–Fisz estimation of evolutionary wavelet spectra
Author(s) -
Fryzlewicz Piotr,
Nason Guy P.
Publication year - 2006
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2006.00558.x
Subject(s) - haar , estimator , piecewise , wavelet , haar wavelet , gaussian , mathematics , series (stratigraphy) , variance (accounting) , wavelet transform , discrete wavelet transform , algorithm , computer science , statistics , artificial intelligence , mathematical analysis , physics , paleontology , accounting , quantum mechanics , business , biology
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 scaled χ 2 ‐data and bringing their distribution close to Gaussianity.