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

Abstract

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 $\textit{community}$-$\alpha$ 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 $\textit{ Red, Blue}$ and $\textit{Swing}$ states throughout presidential elections in the USA. Our analysis suggests interesting global and communal effects.