  In economic and financial applications, there is often the need for analysing
multivariate time series, comprising of time series for a range of quantities.
In some applications such complex systems can be associated with some
underlying network describing pairwise relationships among the quantities.
Accounting for the underlying network structure for the analysis of this type
of multivariate time series is required for assessing estimation error and can
be particularly informative for forecasting. Our work is motivated by a dataset
consisting of time series of industry-to-industry transactions. In this
example, pairwise relationships between Standard Industrial Classification
(SIC) codes can be represented using a network, with SIC codes as nodes and
pairwise transactions between SIC codes as edges, while the observed time
series of the amounts of the transactions for each pair of SIC codes can be
regarded as time-varying weights on the edges. Inspired by Knight et al.
(2020), we introduce the GNAR-edge model which allows modelling of multiple
time series utilising the network structure, assuming that each edge weight
depends not only on its past values, but also on past values of its
neighbouring edges, for a range of neighbourhood stages. The method is
validated through simulations. Results from the implementation of the GNAR-edge
model on the real industry-to-industry data show good fitting and predictive
performance of the model. The predictive performance is improved when
sparsifying the network using a lead-lag analysis and thresholding edges
according to a lead-lag score.
