Abstract

Modeling multivariate time series (MTS) is critical in modern intelligent systems. The accurate forecast of MTS data is still challenging due to the complicated latent variable correlation. Recent works apply the Graph Neural Networks (GNNs) to the task, with the basic idea of representing the correlation as a static graph. However, predicting with a static graph causes significant bias because the correlation is time-varying in the real-world MTS data. Besides, there is no gap analysis between the actual correlation and the learned one in their works to validate the effectiveness. This paper proposes a temporal polynomial graph neural network (TPGNN) for accurate MTS forecasting, which represents the dynamic variable correlation as a temporal matrix polynomial in two steps. First, we capture the overall correlation with a static matrix basis. Then, we use a set of time-varying coefficients and the matrix basis to construct a matrix polynomial for each time step. The constructed result empirically captures the precise dynamic correlation of six synthetic MTS datasets generated by a non-repeating random walk model. Moreover, the theoretical analysis shows that TPGNN can achieve perfect approximation under a commutative condition. We conduct extensive experiments on two traffic datasets with prior structure and four benchmark datasets. The results indicate that TPGNN achieves the state-of-the-art on both short-term and long-term MTS forecastings.