We propose a method - Frequency extracted hierarchical decomposition (FEHD) - for studying multivariate time series that identifies linear combinations of its components that possess a causally hierarchical structure - the method orders the components so that those at the “top” of the hierarchy drive those below. The method shares many of the features of the “hierarchical decomposition” method of Repucci et al. (Annals of Biomedical Engineering, 29, 1135–1149, 2001) but makes a crucial advance - the proposed method is capable of determining this causal hierarchy over arbitrarily specified frequency bands. Additionally, a novel minimization strategy is used to generate the decomposition resulting in an increase in stability, reliability, and an improvement in the sensitivity to model parameters. We demonstrate the utility of the method by applying it to both artificial time series constructed to have specific causal graphs, and to the EEG of healthy volunteers and patient subjects who are recovering from a severe brain injury.

中文翻译：

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一种将多元时间序列分解为特定频带内的因果层次的方法。

我们提出了一种方法-频率提取分层分解（FEHD）-用于研究多元时间序列，以识别具有因果分层结构的组件的线性组合-该方法对组件进行排序，以使层次结构的“顶部”驱动组件下面。该方法具有Repucci等人的“层次分解”方法的许多功能。（生物医学工程年鉴，29（1135-1149年，2001年），但取得了重大进展-所提出的方法能够确定任意指定频段上的这种因果层次。另外，一种新颖的最小化策略被用于生成分解，从而导致稳定性，可靠性的提高以及对模型参数的敏感性的提高。我们通过将该方法应用于构造成具有特定因果图的人工时间序列以及健康志愿者和正在从严重脑损伤中恢复的患者的EEG上，证明了该方法的实用性。