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Bayesian Wavelet Shrinkage of the Haar-Fisz Transformed Wavelet Periodogram

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  • Guy Nason
  • Kara Stevens

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.

Suggested Citation

  • Guy Nason & Kara Stevens, 2015. "Bayesian Wavelet Shrinkage of the Haar-Fisz Transformed Wavelet Periodogram," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-24, September.
    • Handle: RePEc:plo:pone00:0137662
    DOI: 10.1371/journal.pone.0137662
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    References listed on IDEAS

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    1. G. P. Nason & R. Von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
    2. Fryzlewicz, Piotr & van Bellegem, Sébastien & von Sachs, Rainer, 2003. "Forecasting non-stationary time series by wavelet process modelling," LSE Research Online Documents on Economics 25830, London School of Economics and Political Science, LSE Library.
    3. Nason, G.P. & von Sachs, R., 1999. "Wavelets in Time Series Analysis," Papers 9901, Catholique de Louvain - Institut de statistique.
    4. Piotr Fryzlewicz & Sébastien Bellegem & Rainer Sachs, 2003. "Forecasting non-stationary time series by wavelet process modelling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 737-764, December.
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