COVID-19 incidence in the Republic of Ireland: A case study for network-based time series models

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.