Abstract
It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet spectrum of a locally stationary wavelet time series. Our new method works by combining the advantages of a Haar-Fisz transformed spectrum with a simple, but powerful, Bayesian wavelet shrinkage method. Our new method produces excellent and stable spectral estimates and this is demonstrated via simulated data and on differenced infant electrocardiogram data. A major additional benefit of the Bayesian paradigm is that we obtain rigorous and useful credible intervals of the evolving spectral structure. We show how the Bayesian credible intervals provide extra insight into the infant electrocardiogram data.
DOI
10.1371/journal.pone.0137662
Publication Date
2015-09-18
Publication Title
PLOS ONE
Volume
10
Issue
9
Publisher
Public Library of Science (PLoS)
ISSN
1932-6203
Embargo Period
2024-11-22
First Page
e0137662
Last Page
e0137662
Recommended Citation
Nason, G., & Stevens, K. (2015) 'Bayesian Wavelet Shrinkage of the Haar-Fisz Transformed Wavelet Periodogram', PLOS ONE, 10(9), pp. e0137662-e0137662. Public Library of Science (PLoS): Available at: https://doi.org/10.1371/journal.pone.0137662
