Network time series models are increasingly important across many areas, involving known or inferred underlying network structure, which can be exploited to make sense of high-dimensional dynamic phenomena.
We introduce two new association measures: the network and partial network autocorrelation functions and define Corbit (correlation--orbit) visualisation plots. Corbit plots permit interpretation of underlying correlation structures and, crucially, aid model selection more rapidly than general tools such as typical information criteria.
We introduce interpretations of generalised network autoregressive (GNAR) processes as generalised graphical models. We shine new light on how incorporating prior information is related to variable selection and shrinkage in the GNAR context.
We illustrate the usefulness of GNAR models, network autocorrelations and Corbit plots for a novel network time series modelling of COVID--19 mechanical ventilation bed occupancies at 140 NHS Trusts.
We also introduce the R--Corbit plot that shows correlations over different time periods or with respect to external covariates and plots that quantify the relevance and influence of individual nodes. Our analysis provides insight on the COVID--19 series’ underlying dynamics, highlights two groups of geographically co--located `relevant' NHS Trusts, and demonstrates excellent predictive performance.

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• Guy Nason, Imperial College London
• Daniel Salnikov, Imperial College London
• Mario Cortina-Borja, University College London, Institute of Child Health

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