Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks

TLDR

Multivariate time series forecasting relies on inter‑variable dependencies, yet existing methods often miss latent spatial relationships, and although graph neural networks excel at modeling relational data, they require predefined graph structures that are unavailable for such series. This work introduces a general graph neural network framework tailored to multivariate time series data. The framework automatically learns directed variable relations through a graph‑learning module, incorporates external attributes, and employs a mix‑hop propagation layer together with a dilated inception layer to jointly capture spatial and temporal dependencies in an end‑to‑end fashion. Experiments demonstrate that the proposed model surpasses state‑of‑the‑art baselines on three of four benchmark datasets and matches performance on two traffic datasets that provide additional structural information.

Abstract

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.