Network time series are becoming increasingly important across many areas in science and medicine and are often characterised by a known or inferred underlying network structure, which can be exploited to make sense of dynamic phenomena that are often high-dimensional. For example, the Generalised Network Autoregressive (GNAR) models exploit such structure parsimoniously. We use the GNAR framework to introduce two association measures: the network and partial network autocorrelation functions, and introduce Corbit (correlation-orbit) plots for visualisation. As with regular autocorrelation plots, Corbit plots permit interpretation of underlying correlation structures and, crucially, aid model selection more rapidly than using other tools such as AIC or BIC. We additionally interpret GNAR processes as generalised graphical models, which constrain the processes' autoregressive structure and exhibit interesting theoretical connections to graphical models via utilization of higher-order interactions. We demonstrate how incorporation of prior information is related to performing variable selection and shrinkage in the GNAR context. We illustrate the usefulness of the GNAR formulation, network autocorrelations and Corbit plots by modelling a COVID-19 network time series of the number of admissions to mechanical ventilation beds at 140 NHS Trusts in England & Wales. We introduce the Wagner plot that can analyse correlations over different time periods or with respect to external covariates. In addition, we introduce plots that quantify the relevance and influence of individual nodes. Our modelling provides insight on the underlying dynamics of the COVID-19 series, highlights two groups of geographically co-located `influential' NHS Trusts and demonstrates superior prediction abilities when compared to existing techniques.

翻译：网络时间序列在科学和医学的众多领域中正变得日益重要，其通常以已知或推断出的底层网络结构为特征，这种结构可被利用来理解往往高维的动态现象。例如，广义网络自回归模型（GNAR）以简洁的方式利用这种结构。我们基于GNAR框架引入两种关联度量：网络自相关函数和偏网络自相关函数，并引入Corbit（相关轨道）图进行可视化。与常规自相关图类似，Corbit图可解释底层相关结构，且关键的是，相较AIC或BIC等其他工具，能更快速地辅助模型选择。此外，我们将GNAR过程解释为广义图模型，该模型约束了过程的自回归结构，并通过利用高阶交互与图模型展现出有趣的理论关联。我们展示了在GNAR背景下，先验信息的纳入如何与变量选择和收缩相关联。通过建模英格兰与威尔士地区140家NHS信托机构机械通气床位入院人数的COVID-19网络时间序列，我们阐明了GNAR公式、网络自相关和Corbit图的实用性。我们引入Wagner图以分析不同时间段或相对于外部协变量的相关性。同时，引入量化单个节点相关性和影响力的可视化图表。我们的建模揭示了COVID-19序列的底层动态机制，凸显了两组地理共置的"具有影响力"NHS信托机构，并证明了相较于现有技术的预测优越性。