Network-based Time Series models have experienced a surge in popularity over the past years due to their ability to model temporal and spatial dependencies such as arising from the spread of an infectious disease. As statistical models for network time series, generalised network autoregressive (GNAR) models have been introduced. GNAR models are vertex-based models which have an autoregressive component modelling temporal dependence and a spatial autoregressive component to incorporate dependence between neighbouring vertices in the network. This paper compares the performance of GNAR models with different underlying networks in predicting COVID-19 cases for the 26 counties in the Republic of Ireland. The dataset is separated into subsets according to inter-country movement regulations and categorized into two pandemic phases, restricted and unrestricted. Ten static networks are constructed based on either general or COVID-19 specific approaches. In these networks, vertices represent counties, and edges are built upon neighbourhood relations, such as railway lines. We find that while for the prediction task, no underlying static network is consistently superior for either restricted or unrestricted phase, for pandemic phases with restrictions sparse networks perform better while for unrestricted phases, dense networks explain the data better. GNAR models have higher predictive accuracy than ARIMA models, which ignore the network structure. ARIMA and GNAR models perform similarly in pandemic phases with more lenient or no COVID-19 regulation. These findings indicate evidence of network dependencies in the restricted phase, but not in the unrestricted phase. They also show some robustness regarding the network construction method. An analysis of the residuals justifies the model assumptions for the restricted phase but raises questions for the unrestricted phase.

翻译：基于网络的时间序列模型因能够建模传染病传播等过程产生的时间与空间依赖关系，在过去数年里广受关注。作为网络时间序列的统计模型，广义网络自回归（GNAR）模型已被提出。GNAR模型是基于顶点的模型，包含建模时间依赖的自回归分量，以及纳入网络中相邻顶点之间依赖的空间自回归分量。本文比较了不同底层网络结构的GNAR模型在预测爱尔兰共和国26个郡COVID-19病例数方面的表现。根据跨郡人员流动管控措施将数据集划分为子集，并归类为限制性与非限制性两个大流行阶段。基于一般性方法或COVID-19特定方法构建了十个静态网络。在这些网络中，顶点代表各郡，边基于邻接关系（如铁路线路）建立。研究发现，在预测任务中，无论是限制性还是非限制性阶段，均不存在始终优于其他网络的单一静态网络；在实施限制措施的大流行阶段，稀疏网络表现更佳，而在非限制阶段，密集网络更能解释数据。GNAR模型的预测精度高于忽略网络结构的ARIMA模型。在管控措施较宽松或无管控的大流行阶段，ARIMA与GNAR模型表现相近。这些结果表明限制性阶段存在网络依赖的证据，而非限制阶段则不然，同时也显示出对网络构建方法具有一定鲁棒性。残差分析验证了限制性阶段模型假设的合理性，但对非限制阶段提出了疑问。