A forecasting model designed to separate a time series into its trend and seasonal patterns reported its largest gains on longer prediction horizons. In an arXiv preprint, DecoVAE posted relative reductions of up to 52.68% in CRPS, a score for probabilistic forecasts, and 26.51% in NMAE, a normalized error score. On short-term forecasts, the reported maximum reductions were 14.96% in CRPS and 23.30% in NMAE.
The results came from seven real-world multivariate time-series datasets. The paper asks whether an explicitly decomposed model with component-specific mechanisms can improve probabilistic forecasting accuracy and computational efficiency. Forecast quality was evaluated with CRPS and NMAE, and the tabulated results were reported as means plus or minus standard error from three independent retraining and evaluation runs. The study also reports ablations of trend regularization and comparisons of seasonal parameterizations and decomposition methods.
A model that splits the signal
DecoVAE uses two streams. The trend stream works in the time domain and applies latent smoothness regularization, while the seasonal stream works in the frequency domain with a complex Gaussian variational autoencoder, or VAE, used for the seasonal component. In this design, the model gives the slow-moving and repeating parts of a series different internal treatments. The trend is extracted with a moving-average method; the paper compares that choice with FEDFormer's MoE and EMA alternatives in its appendix. For the seasonal module, the authors selected a FITS-based parameterization as the default.
The paper also makes a theoretical claim about the trend penalty. It says the HP-inspired penalty is equivalent to the classical HP objective when decoding is linear, and that it preserves negligible high-frequency trend energy for Lipschitz decoders.
Where the reported numbers were strongest
On short-term benchmarks, DecoVAE had the paper's best average rank for both measures: 1.429 for CRPS and 1.143 for NMAE. The paper also reports the best Electricity NMAE at 0.104 plus or minus 0.001.
The long-term comparison highlighted the paper's biggest single result: up to an 81.11% CRPS improvement over LaST on ETTh2. The reported Electricity NMAE was 0.138 plus or minus 0.001, while Weather recorded the best reported NMAE at 0.459 plus or minus 0.005.
The accuracy results were accompanied by a smaller reported computational footprint. Against K² VAE, the paper reports training that was 30% to 74% faster per epoch and inference that was 10% to 35% faster. Test-memory use was 48% to 85% lower, while model size was 80% to 93% smaller. These ranges describe the selected efficiency comparisons in the paper.
A visual case for interpretability
Interpretability is another part of the proposal. The authors show forecasts with explicit trend and seasonal components and report highly separable trend and seasonal embedding groups in a PCA visualization. The projection makes the separation visible across the model's internal representations. The paper treats that clustering as potentially indicative rather than validated.
The ablation tested the strength of the trend penalty. With first-order regularization set to zero, CRPS was 0.33 and NMAE was 0.39. At first-order strengths from 0.5 to 7.0, the paper associates the settings with approximately 9% and 8% improvements and scores near 0.30 and 0.36. It also reports second-order gains for strengths from 1.0 to 5.0. Here, regularization means the strength assigned to the trend penalty.
Still a preprint
DecoVAE is presented as an arXiv preprint. The manuscript is identified as version 3 and dated 25 Sep 2026. Its reported scores come from the paper's benchmark protocol and three independent retraining and evaluation runs, so the results describe performance under that test setup.
Paper data and sources
Original title: DecoVAE: a Lightweight Interpretable Trend-Seasonal VAE Framework for Efficient Probabilistic Time Series Forecasting
Authors: Alexander Marusov, Dmitry Anikin, Alexey Zaytsev
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text