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, while the observed time series for each pair of SIC codes can be regarded as time-varying weights on the edges. Inspired by Knight et al. (2019), 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.

翻译：在经济与金融应用中，常需分析由多种数量时间序列构成的多维时间序列。在某些场景中，这类复杂系统可关联至描述各变量间配对关系的基础网络。在分析此类多维时间序列时，需考虑底层网络结构以评估估计误差，这对预测尤为关键。本研究源于一组行业间交易时间序列数据：在此实例中，标准产业分类（SIC）代码间的配对关系可表示为网络，其中SIC代码为节点，各代码对的观测时间序列则为边上的时变权重。受Knight等（2019）启发，我们提出GNAR-edge模型，该模型可利用网络结构对多个时间序列进行建模，假设各边权重不仅取决于其历史值，还受多阶邻域内相邻边历史值的影响。通过仿真验证了方法的有效性。将该模型应用于真实行业间交易数据的结果表明，模型具有良好拟合性能与预测能力。采用领先-滞后分析筛选网络，并根据领先-滞后分数设定边阈值进行稀疏化处理后，模型预测性能得到进一步提升。