线性和非线性相关的瞬时和滞后测量 多元时间序列组间：频率分解

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摘要翻译：
定义了任意数目的多元时间序列之间的线性相关性（相干性）和非线性相关性（相位同步性）的测度。测度表示为滞后依赖和瞬时依赖之和。度量值是非负的，并且只有在相关类型独立时才取值为零。这些测度定义在频域内，适用于平稳和非平稳时间序列。这些新结果大大扩展和改进了以前的技术报告(Pascual-Marqui2007,arxiv:0706.1776[stat.me],http://arxiv.org/abs/0706.1776)中提出的结果，并且主要受到Geweke关于线性反馈的开创性论文（1982 JASA 77：304-313）的推动。其中一个重要的应用领域是神经生理学，时间序列由大脑几个位置的神经元电活动组成。相干性和相位同步被解释为位置之间的“连通性”。然而，由于体积传导和低空间分辨率，任何依赖性的度量都高度污染了瞬时的、非生理的贡献。新技术大大消除了这种混杂因素。此外，依赖性的度量可以联合应用于任何数量的大脑区域，即分布的皮层网络，其活动可以用eLORETA估计(Pascual-Marqui2007,ARXIV:0710.3341[math-ph])。
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英文标题：
《Instantaneous and lagged measurements of linear and nonlinear dependence
  between groups of multivariate time series: frequency decomposition》
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作者：
Roberto D. Pascual-Marqui
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最新提交年份：
2007
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
  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]).
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PDF链接：
https://arxiv.org/pdf/711.1455

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关键词：多元时间序列 线性相关 时间序列 非线性 滞后 联合 time frequency 技术