Multivariate time series (MTS) forecasting is crucial in many real-world applications. To achieve accurate MTS forecasting, it is essential to simultaneously consider both intra- and inter-series relationships among time series data. However, previous work has typically modeled intra- and inter-series relationships separately and has disregarded multi-order interactions present within and between time series data, which can seriously degrade forecasting accuracy. In this paper, we reexamine intra- and inter-series relationships from the perspective of mutual information and accordingly construct a comprehensive relationship learning mechanism tailored to simultaneously capture the intricate multi-order intra- and inter-series couplings. Based on the mechanism, we propose a novel deep coupling network for MTS forecasting, named DeepCN, which consists of a coupling mechanism dedicated to explicitly exploring the multi-order intra- and inter-series relationships among time series data concurrently, a coupled variable representation module aimed at encoding diverse variable patterns, and an inference module facilitating predictions through one forward step. Extensive experiments conducted on seven real-world datasets demonstrate that our proposed DeepCN achieves superior performance compared with the state-of-the-art baselines.

翻译：多变量时间序列（MTS）预测在许多实际应用中至关重要。为实现准确的MTS预测，必须同时考虑时间序列数据内部及序列间的相互关系。然而，以往的研究通常分别对序列内部和序列间关系进行建模，且忽略了时间序列数据内部及之间存在的多阶交互作用，这严重降低了预测精度。本文从互信息角度重新审视序列内部与序列间关系，并据此构建了一套全面的关系学习机制，旨在同时捕获复杂的多阶序列内部与序列间耦合关系。基于该机制，我们提出了一种新颖的深度耦合网络DeepCN用于MTS预测，该网络包含三个核心模块：一个专门用于同时显式探索时间序列数据中多阶序列内部与序列间关系的耦合机制；一个用于编码多样变量模式的耦合变量表示模块；以及一个通过单步前向传播实现预测的推理模块。在七个真实数据集上进行的广泛实验表明，我们提出的DeepCN相比当前最先进的基线方法取得了更优越的性能。