  The non-stationary 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 intra-/inter-series
correlations, while time-variant models overlook the intrinsic causes of the
distribution shift. This limits model expressiveness and interpretability of
tackling the distribution shift for MTS forecasting. To mitigate such a
dilemma, we present a unified Probabilistic Graphical Model to Jointly
capturing intra-/inter-series correlations and modeling the time-variant
transitional distribution, and instantiate a neural framework called JointPGM
for non-stationary MTS forecasting. Specifically, JointPGM first employs
multiple Fourier basis functions to learn dynamic time factors and designs two
distinct learners: intra-series and inter-series learners. The intra-series
learner effectively captures temporal dynamics by utilizing temporal gates,
while the inter-series learner explicitly models spatial dynamics through
multi-hop 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 final prediction, and
perform reconstruction. We validate the effectiveness and efficiency of
JointPGM through extensive experiments on six highly non-stationary MTS
datasets, achieving state-of-the-art forecasting performance of MTS
forecasting.
