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：基于网络的时序模型在过去几年中因能够建模传染病传播等时空依赖性而广受欢迎。作为网络时序数据的统计模型，广义网络自回归（GNAR）模型已被引入。GNAR 模型是基于顶点的模型，包含建模时间依赖性的自回归分量和合并网络中相邻顶点之间依赖性的空间自回归分量。本文比较了基于不同底层网络的 GNAR 模型在预测爱尔兰共和国 26 个郡 COVID-19 病例方面的性能。数据集根据跨郡流动法规划分为子集，并分为两个疫情阶段：限制阶段和无限制阶段。基于一般方法或 COVID-19 特定方法构建了十种静态网络。在这些网络中，顶点代表郡，边基于邻里关系（如铁路线）构建。我们发现，对于预测任务，没有任何一种底层静态网络在限制阶段或无限制阶段始终表现更优；在有限制措施的疫情阶段，稀疏网络表现更好，而在无限制阶段，密集网络能更好地解释数据。GNAR 模型比忽略网络结构的 ARIMA 模型具有更高的预测精度。在 COVID-19 法规较宽松或没有法规的疫情阶段，ARIMA 和 GNAR 模型表现相似。这些发现表明，在限制阶段存在网络依赖性证据，但在无限制阶段则没有。它们还显示了网络构建方法的一定稳健性。残差分析验证了限制阶段的模型假设，但对无限制阶段提出了疑问。