  Due to the non-stationary nature, the distribution of real-world multivariate
time series (MTS) changes over time, which is known as distribution drift. Most
existing MTS forecasting models greatly suffer from distribution drift and
degrade the forecasting performance over time. Existing methods address
distribution drift via adapting to the latest arrived data or self-correcting
per the meta knowledge derived from future data. Despite their great success in
MTS forecasting, these methods hardly capture the intrinsic distribution
changes, especially from a distributional perspective. Accordingly, we propose
a novel framework temporal conditional variational autoencoder (TCVAE) to model
the dynamic distributional dependencies over time between historical
observations and future data in MTSs and infer the dependencies as a temporal
conditional distribution to leverage latent variables. Specifically, a novel
temporal Hawkes attention mechanism represents temporal factors subsequently
fed into feed-forward networks to estimate the prior Gaussian distribution of
latent variables. The representation of temporal factors further dynamically
adjusts the structures of Transformer-based encoder and decoder to distribution
changes by leveraging a gated attention mechanism. Moreover, we introduce
conditional continuous normalization flow to transform the prior Gaussian to a
complex and form-free distribution to facilitate flexible inference of the
temporal conditional distribution. Extensive experiments conducted on six
real-world MTS datasets demonstrate the TCVAE's superior robustness and
effectiveness over the state-of-the-art MTS forecasting baselines. We further
illustrate the TCVAE applicability through multifaceted case studies and
visualization in real-world scenarios.
