  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.
