Modelling clusters in network time series with an application to presidential elections in the USA

Network time series are becoming increasingly relevant in the study of dynamic processes characterised by a known or inferred underlying network structure. Generalised Network Autoregressive (GNAR) models provide a parsimonious framework for exploiting the underlying network, even in the high-dimensional setting. We extend the GNAR framework by presenting the $\mathit{\text{community}}$-$\alpha$ GNAR model that exploits prior knowledge and/or exogenous variables for identifying and modelling dynamic interactions across communities in the network. We further analyse the dynamics of $\mathit{\text{Red,}}\mathit{\text{Blue}}$ and $\mathit{\text{Swing}}$ states throughout presidential elections in the USA. Our analysis suggests interesting global and communal effects.