Robust multivariate time series forecasting against intraseries and interseries transitional shift

The nonstationary nature of real-world multivariate time series (MTS) data presents forecasting models with a formidable challenge of the time-variant distribution of time series, referred to as distribution shift. Existing studies on the distribution shift mostly adhere to adaptive normalization techniques for alleviating temporal mean and covariance shifts or time-variant modeling for capturing temporal shifts. Despite improving model generalization, these normalization-based methods often assume a time-invariant transition between outputs and inputs but disregard specific intraseries/interseries correlations, while time-variant models overlook the intrinsic causes of the distribution shift. This limits the model’s expressiveness and interpretability in tackling the distribution shift for MTS forecasting. To mitigate such a dilemma, we present a unified Probabilistic Graphical Model to Jointly capture intraseries/interseries correlations and model the time-variant transitional distribution and instantiate a neural framework called JointPGM for nonstationary MTS forecasting. Specifically, JointPGM first employs multiple Fourier basis functions to learn dynamic time factors and designs two distinct learners: intraseries and interseries learners. The intraseries learner effectively captures temporal dynamics by utilizing temporal gates, while the interseries learner explicitly models spatial dynamics through multihop propagation, incorporating Gumbel-softmax sampling. These two types of series dynamics are subsequently fused into a latent variable, which is inversely employed to infer time factors, generate a final prediction, and perform the reconstruction. We validate the effectiveness and efficiency of JointPGM through extensive experiments on six highly nonstationary MTS datasets, achieving state-of-the-art (SOTA) forecasting performance of MTS forecasting.