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Lightweight Online Adaption for Time Series Foundation Model Forecasts
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Proposes ELF, a lightweight online method that adapts frozen time series foundation model forecasts by ensembling them with a closed-form, Fourier-domain linear forecaster and a fast/slow exponential-weighting combiner.
Problem
Time series foundation models are fixed at deployment and cannot adapt forecasts to shifting data, while existing online adaptation (retraining or continual finetuning) is computationally prohibitive.
Approach
Leave FM weights untouched and instead adapt its forecasts: an online linear ELF-Forecaster in the Fourier domain, refit in closed form via the Woodbury identity, is combined with the FM forecast by an ELF-Weighter that mixes fast and slow exponential-weighting components.
Key results
- ELF improved MASE for every tested FM across all datasets and horizons (negative deltas in all cells of the main table), with VisionTS gaining over 10% on average.
- TTM+ELF outperformed TAFAS, FSNet, OneNet and OneNet-TTM on all nine datasets, at about 0.38 s per update versus 3.76 s for TAFAS (10x faster).
- ELF was reported as 2506x faster than continually finetuning TTM and achieved an average 5.89% gain on ETT datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add ELF forecast adaptation to the foundation model | Time-series FMs (TTM, TimesFM, VisionTS, Chronos, Moirai) · ETTh1, ETTh2, ETTm1, ETTm2, US Weather, Weather, Solar, ECL, Traffic; horizons 30, 96, 336 | MASE: negative MASE differences in every reported +ELF cell | Helped |
| Add ELF forecast adaptation to TTM | TTM · ETTh1, ETTh2, ETTm1, ETTm2, US-Weather, Weather, Solar, ECL, Traffic | rel. MASE | Helped |
| Use both fast and slow weighters rather than either individually (ablation) | ELF-Weighter · Time-series FM forecasting | forecast performance | Helped |
| Replace the ELF-Forecaster with other forecaster types, including FSNet or an FM-residual forecaster (ablation) | ELF · Time-series forecasting | forecast performance | Hurt |
| Filter high-frequency components in the ELF-Forecaster (ablation) | ELF · Time-series forecasting | forecast performance | No clear effect |
| Use the Woodbury matrix identity for online fitting (ablation) | ELF-Forecaster · Time-series forecasting | forecast performance | No clear effect |
| Update ELF more frequently (ablation) | ELF · Time-series forecasting | forecast performance | Helped |
Surprising findings
- Using ELF improved every FM on every dataset tested, including the strongest FMs, in the rolling-window setting.
Limitations
- Gains are reported relative to FMs without ELF and depend on hyperparameters fixed a priori (lambda=20, alpha=0.9, eta=0.5, B=5).
- Evaluated only on standard benchmarks with a single fixed context length of 520 and one update interval M=200.
- Requires a warm-up period of 5 update steps before the ELF-Forecaster is used.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Weather US Weather Solar ECL Traffic Wind-PerSec Solar-PerSec Cloud-PerSec
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Weather US Weather Solar ECL Traffic Wind-PerSec Solar-PerSec Cloud-PerSec
Metrics: MASE RMSSE seconds per update step
Baselines: TAFAS FSNet OneNet OneNet-TTM continual finetuning of TTM
Builds on: FITS exponential weighting TAFAS OneNet FSNet
Closest papers by meaning
- SEMPO: Lightweight Foundation Models for Time Series Forecasting (NeurIPS 2025 · similarity 0.87)
- Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models (NeurIPS 2026 · similarity 0.86)
- AdaPTS: Adapting Univariate Foundation Models to Probabilistic Multivariate Time Series Forecasting (ICML 2025 · similarity 0.86)
- OATS: Online Data Augmentation for Time Series Foundation Models (NeurIPS 2026 · similarity 0.86)
- Time-FFM: Towards LM-Empowered Federated Foundation Model for Time Series Forecasting (NeurIPS 2024 · similarity 0.85)
- Less is More: Unlocking Specialization of Time Series Foundation Models via Structured Pruning (NeurIPS 2025 · similarity 0.85)
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