# Accurate Parameter-Efficient Test-Time Adaptation for Time Series Forecasting

arXiv: https://arxiv.org/abs/2506.23424 · HTML: https://mlsanity.com/paper/2506.23424/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 26 references that are in the map.
- First posted on arXiv 29 Jun 2025.

## Builds on (most cited first, 20 of 20)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [AdaptFormer: Adapting Vision Transformers for Scalable Visual Recognition](https://mlsanity.com/paper/2205.13535/) (2022)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [Parameter-free Online Test-time Adaptation](https://mlsanity.com/paper/2201.05718/) (2022)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [Transformers without Normalization](https://mlsanity.com/paper/2503.10622/) (2025)
- [On Pitfalls of Test-Time Adaptation](https://mlsanity.com/paper/2306.03536/) (2023)
- [An Analysis of Linear Time Series Forecasting Models](https://mlsanity.com/paper/2403.14587/) (2024)
- [Battling the Non-stationarity in Time Series Forecasting via Test-time Adaptation](https://mlsanity.com/paper/2501.04970/) (2025)
- [Patch-wise Structural Loss for Time Series Forecasting](https://mlsanity.com/paper/2503.00877/) (2025)
- [Low-Rank Adaptation of Time Series Foundational Models for Out-of-Domain Modality Forecasting](https://mlsanity.com/paper/2405.10216/) (2024)
- [When Model Meets New Normals: Test-time Adaptation for Unsupervised Time-series Anomaly Detection](https://mlsanity.com/paper/2312.11976/) (2023)
- [Channel-Aware Low-Rank Adaptation in Time Series Forecasting](https://mlsanity.com/paper/2407.17246/) (2024)
- [ST-LoRA: Low-rank Adaptation for Spatio-Temporal Forecasting](https://mlsanity.com/paper/2404.07919/) (2024)

## Built on by (most cited first, 14 of 14)

- [The Forecast After the Forecast: A Post-Processing Shift in Time Series](https://mlsanity.com/paper/2601.20280/) (2026)
- [Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models](https://mlsanity.com/paper/2606.14222/) (2026)
- [Towards Principled Test-Time Adaptation for Time Series Forecasting](https://mlsanity.com/paper/2605.17250/) (2026)
- [Online time series prediction using feature adjustment](https://mlsanity.com/paper/2509.03810/) (2025)
- [AdaNODEs: Test Time Adaptation for Time Series Forecasting Using Neural ODEs](https://mlsanity.com/paper/2601.12893/) (2026)
- [Learning from Yesterday's Error: An Efficient Online Learning Method for Traffic Demand Prediction](https://mlsanity.com/paper/2602.21757/) (2026)
- [COMET: Codebook-based Online-adaptive Multi-scale Embedding for Time-series Anomaly Detection](https://mlsanity.com/paper/2602.01635/) (2026)
- [STEPS: A Temporal Smooth Error Propagation Solver on the Manifolds for Test-Time Adaptation in Time Series Forecasting](https://mlsanity.com/paper/2605.08005/) (2026)
- [When Does Online Adaptation Pay on the Edge? A Leakage-Free Evaluation of Warmup, Learning-Rate Selection, and Resource Trade-offs for Time-Series Forecasting](https://mlsanity.com/paper/2609.01126/) (2026)
- [Downside-Controlled Online Forecast Combination under Delayed and Revised Outcomes](https://mlsanity.com/paper/2609.29096/) (2026)
- [EPOC: Endpoint-Preserving Online Correction With Compressed Residual State for Multi-Horizon Time Series Forecasting](https://mlsanity.com/paper/2609.30929/) (2026)
- [Correction-space Cross-variate Interaction for Test-time Adaptation in Time Series Forecasting](https://mlsanity.com/paper/2609.34638/) (2026)
- [Training on the Future: A Delay-Aware Audit of Test-Time Adaptation for Time-Series Forecasting](https://mlsanity.com/paper/2610.12232/) (2026)
- [DPAL: A Test-Time Adaptation Loss for Financial Time Series Forecasting](https://mlsanity.com/paper/2610.14376/) (2026)

## Abstract (arXiv)

Real-world time series often exhibit a non-stationary nature, degrading the performance of pre-trained forecasting models. Test-Time Adaptation (TTA) addresses this by adjusting models during inference, but existing methods typically update the full model, increasing memory and compute costs. We propose PETSA, a parameter-efficient method that adapts forecasters at test time by only updating small calibration modules on the input and output. PETSA uses low-rank adapters and dynamic gating to adjust representations without retraining. To maintain accuracy despite limited adaptation capacity, we introduce a specialized loss combining three components: (1) a robust term, (2) a frequency-domain term to preserve periodicity, and (3) a patch-wise structural term for structural alignment. PETSA improves the adaptability of various forecasting backbones while requiring fewer parameters than baselines. Experimental results on benchmark datasets show that PETSA achieves competitive or better performance across all horizons. Our code is available at: https://github.com/BorealisAI/PETSA