This manuscript presents a novel method for discovering effective connectivity between specified pairs of nodes in a high-dimensional network of time series. To accurately perform Granger causality analysis from the first node to the second node, it is essential to eliminate the influence of all other nodes within the network. The approach proposed is to create a low-dimensional representation of all other nodes in the network using frequency-domain-based dynamic principal component analysis (spectral DPCA). The resulting scores are subsequently removed from the first and second nodes of interest, thus eliminating the confounding effect of other nodes within the high-dimensional network. To conduct hypothesis testing on Granger causality, we propose a permutation-based causality test. This test enhances the accuracy of our findings when the error structures are non-Gaussian. The approach has been validated in extensive simulation studies, which demonstrate the efficacy of the methodology as a tool for causality analysis in complex time series networks. The proposed methodology has also been demonstrated to be both expedient and viable on real datasets, with particular success observed on multichannel EEG networks.

翻译：本文提出了一种新颖方法，用于发现高维时间序列网络中指定节点对之间的有效连通性。为准确执行从第一个节点到第二节点的格兰杰因果分析，必须消除网络中所有其他节点的影响。所提出的方法是通过基于频域的动态主成分分析（谱DPCA）创建网络中所有其他节点的低维表示。随后将得到的得分从关注的第一和第二节点中移除，从而消除高维网络中其他节点的混杂效应。为进行格兰杰因果关系的假设检验，我们提出了一种基于置换的因果检验方法。当误差结构为非高斯分布时，该检验能提高研究结果的准确性。该方法已在大量模拟研究中得到验证，证明了其作为复杂时间序列网络因果分析工具的有效性。所提出的方法在真实数据集上也显示出便捷性和可行性，特别是在多通道脑电图网络中取得了显著成功。