Learning and integration of adaptive hybrid graph structures for multivariate time series forecasting

Recent status-of-the-art methods for multivariate time series forecasting can be categorized into graph-based approach and global-local approach. The former approach uses graphs to represent the dependencies among variables and apply graph neural networks to the forecasting problem. The latter approach decomposes the matrix of multivariate time series into global components and local components to capture the shared information across variables. However, both approaches cannot capture the propagation delay of the dependencies among individual variables of a multivariate time series, for example, the congestion at intersection A has delayed effects on the neighboring intersection B. In addition, graph-based forecasting methods cannot capture the shared global tendency across the variables of a multivariate time series; and global-local forecasting methods cannot reflect the nonlinear inter-dependencies among variables of a multivariate time series. In this paper, we propose to combine the advantages of both approaches by integrating Adaptive Global-Local Graph Structure Learning with Gated Recurrent Units (AGLG-GRU). We learn a global graph to represent the shared information across variables. And we learn dynamic local graphs to capture the local randomness and nonlinear dependencies among variables. We apply diffusion convolution and graph convolution operations to global and dynamic local graphs to integrate the information of graphs and update gated recurrent unit for multivariate time series forecasting. The experimental results on seven representative real-world datasets demonstrate that our approach outperforms various existing methods.