标题： 多变量时间序列组之间线性依赖和非线性依赖的瞬时和滞后测量：频率分解 显示英文标题

标题： Instantaneous and lagged measurements of linear and nonlinear dependence between groups of multivariate time series: frequency decomposition

摘要： 定义了任意数量的多变量时间序列之间的线性依赖（相干性）和非线性依赖（相位同步）的度量。 这些度量表示为滞后依赖性和瞬时依赖性的总和。 这些度量是非负的，并且只有在相关类型的独立性存在时才取值为零。 这些度量是在频域中定义的，并适用于平稳和非平稳时间序列。 这些新结果显著扩展并改进了之前技术报告中提出的结果（Pascual-Marqui 2007, arXiv:0706.1776 [stat.ME], http://arxiv.org/abs/0706.1776），并且主要是受Geweke关于线性反馈的经典论文（1982年JASA 77:304-313）启发。 一个重要的应用领域是神经生理学，其中时间序列由多个大脑位置的电神经活动组成。 相干性和相位同步被解释为位置之间的“连接性”。 然而，由于体积传导和低空间分辨率，任何依赖性的度量都会受到强烈的瞬时、非生理贡献污染。 新技术大大消除了这个混淆因素。 此外，依赖性的度量可以应用于任意数量的大脑区域联合，即分布式皮质网络，其活动可以通过eLORETA估计（Pascual-Marqui 2007, arXiv:0710.3341 [math-ph]）。 显示英文摘要

摘要： Measures of linear dependence (coherence) and nonlinear dependence (phase synchronization) between any number of multivariate time series are defined. The measures are expressed as the sum of lagged dependence and instantaneous dependence. The measures are non-negative, and take the value zero only when there is independence of the pertinent type. These measures are defined in the frequency domain and are applicable to stationary and non-stationary time series. These new results extend and refine significantly those presented in a previous technical report (Pascual-Marqui 2007, arXiv:0706.1776 [stat.ME], http://arxiv.org/abs/0706.1776), and have been largely motivated by the seminal paper on linear feedback by Geweke (1982 JASA 77:304-313). One important field of application is neurophysiology, where the time series consist of electric neuronal activity at several brain locations. Coherence and phase synchronization are interpreted as "connectivity" between locations. However, any measure of dependence is highly contaminated with an instantaneous, non-physiological contribution due to volume conduction and low spatial resolution. The new techniques remove this confounding factor considerably. Moreover, the measures of dependence can be applied to any number of brain areas jointly, i.e. distributed cortical networks, whose activity can be estimated with eLORETA (Pascual-Marqui 2007, arXiv:0710.3341 [math-ph]).