Haar-Fisz estimation of evolutionary wavelet spectra

• 成果类型: Article
• 署名作者: Fryzlewicz, Piotr; Nason, Guy P.
• 署名单位: University of Bristol
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2006.00558.x
• 发表日期: 2006
• 页码: 611-634
• 关键词: locally stationary-processes; quadratic-forms; time-series; moments

摘要

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.