DecoVAE: Decomposing Predictable Dynamics and Uncertainty for Efficient Probabilistic Time Series Forecasting

Probabilistic forecasting of multivariate time series remains challenging because accurate prediction requires modeling both structured temporal dynamics and time-varying residual uncertainty. Existing methods may treat these sources uniformly or incur substantial computational overhead, making it difficult to jointly achieve accurate and efficient forecasting. We propose DecoVAE, a lightweight Trend–Seasonality–Residual variational framework that assigns distinct statistical roles to structured dynamics and residual uncertainty. Trend and seasonality determine the forecast mean, whereas the residual stream models its time-varying variance rather than predicting residual realizations directly. To reflect their different structures, DecoVAE represents trend through a smoothness-regularized latent trajectory, seasonality through a frequency-domain VAE, and residual uncertainty through a dedicated volatility stream. Across seven real-world datasets, DecoVAE achieves the lowest mean CRPS on every dataset, with average relative improvements over the strongest competing method of 10.05% for short-term and 12.28% for long-term forecasting, while remaining competitive in point accuracy (NMAE). Compared with the closest competing method, DecoVAE trains approximately $3\times$ faster and is about $7.2\times$ smaller on high-dimensional datasets. These results suggest that assigning distinct statistical roles to structured temporal dynamics and residual uncertainty enables accurate and efficient probabilistic time series forecasting.