Multivariate time series is prevalent in many scientific and industrial domains. Modeling multivariate signals is challenging due to their long-range temporal dependencies and intricate interactions--both direct and indirect. To confront these complexities, we introduce a method of representing multivariate signals as nodes in a graph with edges indicating interdependency between them. Specifically, we leverage graph neural networks (GNN) and attention mechanisms to efficiently learn the underlying relationships within the time series data. Moreover, we suggest employing hierarchical signal decompositions running over the graphs to capture multiple spatial dependencies. The effectiveness of our proposed model is evaluated across various real-world benchmark datasets designed for long-term forecasting tasks. The results consistently showcase the superiority of our model, achieving an average 23\% reduction in mean squared error (MSE) compared to existing models.

翻译：多变量时间序列在众多科学和工业领域中普遍存在。由于信号具有长程时间依赖性和错综复杂的相互作用（包括直接与间接关系），对其建模极具挑战性。为应对这些复杂性，我们提出了一种方法，将多变量信号表示为图中的节点，并以边来表示信号间的相互依赖关系。具体而言，我们利用图神经网络与注意力机制，高效学习时间序列数据中的潜在关系。此外，我们建议采用在图结构上运行的层次化信号分解方法，以捕获多种空间依赖性。我们在多个面向长期预测任务的真实世界基准数据集上评估了所提模型的有效性。结果一致表明，该模型具有优越性，相较于现有模型，平均均方误差降低了23%。