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In economic and financial applications, there is often the need for analysingmultivariate time series, comprising of time series for a range of quantities.In some applications such complex systems can be associated with someunderlying network describing pairwise relationships among the quantities.Accounting for the underlying network structure for the analysis of this typeof multivariate time series is required for assessing estimation error and canbe particularly informative for forecasting. Our work is motivated by a datasetconsisting of time series of industry-to-industry transactions. In thisexample, pairwise relationships between Standard Industrial Classification(SIC) codes can be represented using a network, with SIC codes as nodes andpairwise transactions between SIC codes as edges, while the observed timeseries of the amounts of the transactions for each pair of SIC codes can beregarded as time-varying weights on the edges. Inspired by Knight et al.(2020), we introduce the GNAR-edge model which allows modelling of multipletime series utilising the network structure, assuming that each edge weightdepends not only on its past values, but also on past values of itsneighbouring edges, for a range of neighbourhood stages. The method isvalidated through simulations. Results from the implementation of the GNAR-edgemodel on the real industry-to-industry data show good fitting and predictiveperformance of the model. The predictive performance is improved whensparsifying the network using a lead-lag analysis and thresholding edgesaccording to a lead-lag score.

The GNAR-edge model: A network autoregressive model for networks with time-varying edge weights