Bayesian Wavelet Shrinkage of the Haar-Fisz Transformed Wavelet Periodogram.
Bayesian Wavelet Shrinkage of the Haar-Fisz Transformed Wavelet Periodogram.
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DOI：
10.1371/journal.pone.0137662
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发表时间：
2015
期刊：
影响因子：
3.7
通讯作者：
Stevens K
中科院分区：
文献类型：
--
作者：
Nason G;Stevens K
人们越来越认识到，许多真实的世界时间序列是不稳定的，并表现出不断发展的二阶自协方差或频谱结构。本文介绍了一种贝叶斯方法建模的局部平稳小波时间序列的演变小波谱。我们的新方法的工作原理相结合的Haar-Fisz变换频谱的优点，一个简单的，但功能强大，贝叶斯小波收缩方法。我们的新方法产生优秀和稳定的频谱估计，这是通过模拟数据和不同的婴儿心电图数据证明。贝叶斯范式的一个主要的额外好处是，我们得到严格的和有用的可信区间的不断发展的光谱结构。我们展示了如何贝叶斯可信区间提供额外的洞察婴儿心电图数据。
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.