# Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models

arXiv: https://arxiv.org/abs/2606.14222 · HTML: https://mlsanity.com/paper/2606.14222/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 82 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 30 of 60)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (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)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [MAD-X: An Adapter-Based Framework for Multi-Task Cross-Lingual Transfer](https://mlsanity.com/paper/2005.00052/) (2020)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [GIFT-Eval: A Benchmark For General Time Series Forecasting Model Evaluation](https://mlsanity.com/paper/2410.10393/) (2024)
- [Timer: Generative Pre-trained Transformers Are Large Time Series Models](https://mlsanity.com/paper/2402.02368/) (2024)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Chronos-2: From Univariate to Universal Forecasting](https://mlsanity.com/paper/2510.15821/) (2025)
- [Sundial: A Family of Highly Capable Time Series Foundation Models](https://mlsanity.com/paper/2502.00816/) (2025)
- [TimeGPT-1](https://mlsanity.com/paper/2310.03589/) (2023)
- [Tiny Time Mixers (TTMs): Fast Pre-trained Models for Enhanced Zero/Few-Shot Forecasting of Multivariate Time Series](https://mlsanity.com/paper/2401.03955/) (2024)
- [TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning](https://mlsanity.com/paper/2505.23719/) (2025)
- [Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2310.08278/) (2023)

## Built on by (most cited first, 9 of 9)

- [LLM-based Agents for Forecasting and Prediction: Methods, Training, Evaluation, and Applications](https://mlsanity.com/paper/2608.23058/) (2026)
- [When Do Corrective Features Help? An Agent for Corrective Feature Discovery on Black-Box Forecasters](https://mlsanity.com/paper/2608.05207/) (2026)
- [Systematic Evaluation of TabPFN-TS and Chronos-2 for Zero-Shot Heat Load Forecasting in District Heating Networks](https://mlsanity.com/paper/2608.20024/) (2026)
- [Downside-Controlled Online Forecast Combination under Delayed and Revised Outcomes](https://mlsanity.com/paper/2609.29096/) (2026)
- [Pythia: Toward Foundation World Models for Multimodal Time Series](https://mlsanity.com/paper/2610.05240/) (2026)
- [A Unified Scaling Law for Time Series Foundation Models](https://mlsanity.com/paper/2610.05269/) (2026)
- [The Premise Is the Problem: Exchangeability Failure in Self-Monitored Test-Time Adaptation](https://mlsanity.com/paper/2610.07038/) (2026)
- [Training on the Future: A Delay-Aware Audit of Test-Time Adaptation for Time-Series Forecasting](https://mlsanity.com/paper/2610.12232/) (2026)
- [ECHO: Correcting Time Series Foundation Model Forecasts with Historical Analogues and Errors](https://mlsanity.com/paper/2610.16433/) (2026)

## Abstract (arXiv)

The rapid evolution of Time Series Foundation Models (TSFMs) has advanced zero-shot forecasting across diverse domains. Inspired by the current form of Large Language Models, future TSFMs may be offered as commercialized, closed-source API services. However, many existing online adaptation methods still rely on white-box access for parameter fine-tuning or gradient backpropagation. This paradigm mismatch raises a question: In black-box online adaptation for TSFMs, what should we learn? We answer this with an insight: the predictive errors of the base model are conditioned on both the input and output of the base model (i.e., the context of errors). To validate this insight, we propose ORCA (Online Residual Contextual Adaptation). We conduct extensive experiments across 5 state-of-the-art TSFMs and 8 datasets to demonstrate the effectiveness of our approach. Furthermore, through ablation studies, we quantitatively analyze the impact of different adapter learning hypotheses on the final adaptation performance in black-box online adaptation. Code available at https://github.com/Fifthky/ORCA.