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Enhancing Zero-Shot Time Series Forecasting in Off-the-Shelf LLMs via Noise Injection Prompting

Paper · 2026 · Xingyou Yin, Ceyao Zhang, Min Hu et al.

Summary

Frozen, off-the-shelf LLMs can forecast time series (TS) zero-shot when numbers are serialized as text, as in LLMTime. Because no parameters are updated, however, their forecasts are sensitive to the exact numeric string and to distribution shift. The authors propose NLTS (Noise-injected LLM for Time Series), which adds small zero-mean random noise to the raw series before converting it to text and tokens. The frozen model then continues the sequence by ordinary next-token generation. The procedure is repeated over several independently perturbed copies of the input, and the median of the resulting forecasts is the point prediction, with the spread across samples used as an uncertainty estimate. The approach needs no gradients, no fine-tuning and no access to model internals. The paper motivates the effect theoretically and evaluates it on standard benchmarks with several LLMs, reporting consistent accuracy gains. To rule out memorization from pre-training data, the authors also assemble evaluation sets that postdate or lie outside the models' training data, where NLTS still beats the baselines. This suggests that LLM forecasting skill is not merely contamination.

Key points

  • Method: NLTS works as an inference-time augmentation. Gaussian noise and four other zero-mean noise distributions are tested, and textualization keeps a one-to-one mapping between numbers and tokens. Code is at github.com/jkumh/NLTS.
  • Contamination-free data, part 1: Synthetic GP series use six kernels (ExpSineSquared, Linear, Matérn, Polynomial, RQ, RBF). Recent stock data covers DJIAh (hourly, May 1 to July 31, 2025) and SZ300m (minute-level, May 6–9, 2025).
  • Contamination-free data, part 2: Private 5G wireless traffic data covers online users and traffic volume. Smart-glasses accelerometer data comes from UESTC-MMEA-CL (3-axis).
  • Results: On these sets, NLTS built on GPT-3.5-Turbo-Instruct outperforms baselines such as NSTransformer, Autoformer and ARIMA in MSE and MAE. LLMTime is also competitive.
  • Benchmark observation: Several specialized deep TS models underperform ARIMA on the new data. The authors take this as a sign that conventional TS benchmarks may be outdated.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓Peking UniversityBeijing · China315 works · 43,268 citations🎓Central South UniversityChangsha · China23 works · 657 citations

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 18,614 worksDecision Sciences · 249 worksSignal Processing · 493 worksManagement Science and Operations Research · 134 works

🧭 Topics 1Research subjects and languages the work is about.Language models & pretraining · 3,894 works

Cite

Cite as Xingyou Yin, Ceyao Zhang, Min Hu and Kai Chen. 2026. Enhancing Zero-Shot Time Series Forecasting in Off-the-Shelf LLMs via Noise Injection Prompting. Findings of the Association for Computational Linguistics: ACL 2026.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.findings-acl.2054

@inproceedings{yin2026enhancing,
  title = {{Enhancing Zero-Shot Time Series Forecasting in Off-the-Shelf LLMs via Noise Injection Prompting}},
  author = {Xingyou Yin, Ceyao Zhang, Min Hu and Kai Chen},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.2054},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.2054}
}

References

49 references, 10 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. Samira Abnar, Mostafa Dehghani, Behnam Neyshabur, and Hanie Sedghi. 2021. Exploring the limits of large scale pre-training. arXiv preprint arXiv:2110.02095. — [arXiv:2110.02095](https://arxiv.org/abs/2110.02095) find
  2. Anthropic. 2024. Claude 3.5 sonnet model card addendum. https://www-cdn.anthropic.com/ fed9cc193a14b84131812372d8d5857f8f304c52/ Model_Card_Claude_3_Addendum.pdf. Accessed: 2024-06-23. ↗
  3. George EP Box and Gwilym M Jenkins. 1968. Some recent advances in forecasting and control. Journal of the Royal Statistical Society. Series C (Applied Statistics), 17(2):91–109. find
  4. Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, and 1 others. 2020. Language models are few-shot learners. Advances in neural information processing systems, 33:1877–1901.
  5. Defu Cao, Furong Jia, Sercan O Arik, Tomas Pfister, Yixiang Zheng, Wen Ye, and Yan Liu. Tempo: Prompt-based generative pre-trained transformer for time series forecasting. In The Twelfth International Conference on Learning Representations. find
  6. Ching Chang, Wei-Yao Wang, Wen-Chih Peng, and Tien-Fu Chen. 2025. Llm4ts: Aligning pre-trained llms as data-efficient time-series forecasters. ACM Transactions on Intelligent Systems and Technology, 16(3):1–20. find
  7. Zhengping Che, Sanjay Purushotham, Kyunghyun Cho, David Sontag, and Yan Liu. 2018. Recurrent neural networks for multivariate time series with missing values. Scientific reports, 8(1):6085. find
  8. Kai Chen, Qinglei Kong, Yijue Dai, Yue Xu, Feng Yin, Lexi Xu, and Shuguang Cui. 2022. Recent advances in data-driven wireless communication using gaussian processes: a comprehensive survey. China Communications, 19(1):218–237. find
  9. Yijue Dai, Tianjian Zhang, Zhidi Lin, Feng Yin, Sergios Theodoridis, and Shuguang Cui. 2020. An interpretable and sample efficient deep kernel for gaussian process. In Conference on Uncertainty in Artificial Intelligence, pages 759–768. PMLR. find
  10. DeepSeek-AI, Aixin Liu, Bei Feng, Bing Xue, Bingxuan Wang, Bochao Wu, Chengda Lu, Chenggang Zhao, and 1 others. 2024. Deepseek-v3 technical report. find
  11. Yihong Dong, Xue Jiang, Huanyu Liu, Zhi Jin, Bin Gu, Mengfei Yang, and Ge Li. 2024. Generalization or memorization: Data contamination and trustworthy evaluation for large language models. In Findings of the Association for Computational Linguistics: ACL 2024, pages 12039–12050. find
  12. Jianbo Gao, Hussain Sultan, Jing Hu, and Wen-Wen Tung. 2009. Denoising nonlinear time series by adaptive filtering and wavelet shrinkage: a comparison. IEEE signal processing letters, 17(3):237–240. find
  13. Team GLM, Aohan Zeng, Bin Xu, Bowen Wang, Chenhui Zhang, Da Yin, Dan Zhang, Diego Rojas, Guanyu Feng, Hanlin Zhao, and 1 others. 2024. Chatglm: A family of large language models from glm-130b to glm-4 all tools. arXiv preprint arXiv:2406.12793.
  14. Nate Gruver, Marc Finzi, Shikai Qiu, and Andrew G Wilson. 2023. Large language models are zero-shot time series forecasters. In Advances in Neural Information Processing Systems, volume 36, pages 19622– 19635. Curran Associates, Inc.
  15. Julien Herzen, Francesco Lässig, Samuele Giuliano Piazzetta, Thomas Neuer, Léo Tafti, Guillaume Raille, Tomas Van Pottelbergh, Marek Pasieka, Andrzej Skrodzki, Nicolas Huguenin, and 1 others. 2022. Darts: User-friendly modern machine learning for time series. Journal of Machine Learning Research, 23… find
  16. Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y Zhang, Xiaoming Shi, Pin-Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, and 1 others. 2023a. Time-llm: Time series forecasting by reprogramming large language models. arXiv preprint arXiv:2310.01728.
  17. Ming Jin, Qingsong Wen, Yuxuan Liang, Chaoli Zhang, Siqiao Xue, Xue Wang, James Zhang, Yi Wang, Haifeng Chen, Xiaoli Li, and 1 others. 2023b. Large models for time series and spatio-temporal data: A survey and outlook. arXiv preprint arXiv:2310.10196. — [arXiv:2310.10196](https://arxiv.org/abs/2310.10196) find
  18. Gyu Il Kim and Kyungyong Chung. 2024. Extraction of features for time series classification using noise injection. Sensors, 24(19):6402. find
  19. Colin Lea, Rene Vidal, Austin Reiter, and Gregory D Hager. 2016. Temporal convolutional networks: A unified approach to action segmentation. In Computer Vision–ECCV 2016 Workshops: Amsterdam, The Netherlands, October 8-10 and 15-16, 2016, Proceedings, Part III 14, pages 47–54, Amsterdam, The Netherl… find
  20. Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. 2015. Deep learning. nature, 521(7553):436–444. find
  21. Haoxin Liu, Zhiyuan Zhao, Jindong Wang, Harshavardhan Kamarthi, and B Aditya Prakash. 2024. Lstprompt: Large language models as zero-shot time series forecasters by long-short-term prompting. In Findings of the Association for Computational Linguistics: ACL 2024, pages 7832–7840. find
  22. Vahid Nourani and Afshin Partoviyan. 2018. Hybrid denoising-jittering data pre-processing approach to enhance multi-step-ahead rainfall–runoff modeling. Stochastic environmental research and risk assessment, 32(2):545–562. find
  23. OpenAI. 2023. Gpt-4 technical report.
  24. Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, and 1 others. 2019. Language models are unsupervised multitask learners. OpenAI blog, 1(8):9. find
  25. Chenxi Sun, Hongyan Li, Yaliang Li, and Shenda Hong. 2024. Test: Text prototype aligned embedding to activate llm’s ability for time series. In The Twelfth International Conference on Learning Representations, Vienna, Austria. OpenReview.net. find
  26. Peiyuan Liu, Hang Guo, Tao Dai, Naiqi Li, Jigang Bao, Xudong Ren, Yong Jiang, and Shu-Tao Xia. 2025. Calf: Aligning llms for time series forecasting via cross-modal fine-tuning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 18915–18923. find
  27. Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, and 1 others. 2023. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288.
  28. Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, and Mingsheng Long. 2023. itransformer: Inverted transformers are effective for time series forecasting. arXiv preprint arXiv:2310.06625. — [arXiv:2310.06625](https://arxiv.org/abs/2310.06625) find
  29. Patara Trirat, Yooju Shin, Junhyeok Kang, Youngeun Nam, Jihye Na, Minyoung Bae, Joeun Kim, Byunghyun Kim, and Jae-Gil Lee. 2024. Universal time-series representation learning: A survey. arXiv preprint arXiv:2401.03717. — [arXiv:2401.03717](https://arxiv.org/abs/2401.03717) find
  30. Yong Liu, Haixu Wu, Jianmin Wang, and Mingsheng Long. 2022. Non-stationary transformers: Exploring the stationarity in time series forecasting. Advances in neural information processing systems, 35:9881– 9893. find
  31. Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang, and Mingsheng Long. 2023. Timesnet: Temporal 2d-variation modeling for general time series analysis. In The Eleventh International Conference on Learning Representations. find
  32. Qianli Ma, Zhen Liu, Zhenjing Zheng, Ziyang Huang, Siying Zhu, Zhongzhong Yu, and James T. Kwok. 2024. A survey on time-series pre-trained models. IEEE Transactions on Knowledge and Data Engineering, 36(12):7536–7555. find
  33. Haixu Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. 2021. Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting. Advances in neural information processing systems, 34:22419–22430. find
  34. Aristeidis Magklaras, Nikolaos Andriopoulos, and Alexios Birbas. 2019. Noise injection/machine learning fraud detection framework in time series data. In 25th International Conference on Noise and Fluctuations (ICNF 2019), Neuchâtel, Switzerland. ICLAB. find
  35. Cheng Xu, Shuhao Guan, Derek Greene, M Kechadi, and 1 others. 2024. Benchmark data contamination of large language models: A survey. arXiv preprint arXiv:2406.04244.
  36. Douglas C Montgomery, Cheryl L Jennings, and Murat Kulahci. 2015. Introduction to time series analysis and forecasting. John Wiley & Sons, Hoboken, NJ, USA. find
  37. Yuqi Nie, Nam H Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. 2023a. A time series is worth 64 words: Long-term forecasting with transformers. In The Eleventh International Conference on Learning Representations, Kigali Convention Center, Rwanda. OpenReview.net.
  38. Yuqi Nie, Nam H Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. 2023b. A time series is worth 64 words: Long-term forecasting with transformers. In The Eleventh International Conference on Learning Representations.
  39. Linfeng Xu, Qingbo Wu, Lili Pan, Fanman Meng, Hongliang Li, Chiyuan He, Hanxin Wang, Shaoxu Cheng, and Yu Dai. 2023. Towards continual egocentric activity recognition: A multi-modal egocentric activity dataset for continual learning. IEEE Transactions on Multimedia, 26:2430–2443. find
  40. Linning Xu, Yijue Dai, Jiawei Zhang, Ceyao Zhang, and Feng Yin. 2020. Exact o (n 2) hyper-parameter optimization for gaussian process regression. In 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pages 1–6. IEEE. find
  41. Hao Xue and Flora D Salim. 2023. Promptcast: A new prompt-based learning paradigm for time series forecasting. IEEE Transactions on Knowledge and Data Engineering, 36(11):6851–6864. find
  42. An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, and 1 others. 2025. Qwen3 technical report.
  43. Ailing Zeng, Muxi Chen, Lei Zhang, and Qiang Xu. 2023. Are transformers effective for time series forecasting? In Proceedings of the AAAI conference on artificial intelligence, volume 37, pages 11121– 11128. find
  44. Ceyao Zhang, Tianjian Zhang, Feng Yin, and Abdelhak M Zoubir. 2023. Data-adaptive m-estimators for robust regression via bi-level optimization. Signal Processing, 210:109063. find
  45. G Peter Zhang. 2007. A neural network ensemble method with jittered training data for time series forecasting. Information Sciences, 177(23):5329–5346. find
  46. Tianjian Zhang, Feng Yin, and Zhi-Quan Luo. 2021. Fast generic interaction detection for model interpretability and compression. In International Conference on Learning Representations. find
  47. Yushun Zhang, Congliang Chen, Tian Ding, Ziniu Li, Ruoyu Sun, and Zhi-Quan Luo. 2024. Why transformers need adam: A hessian perspective. Advances in neural information processing systems, 37:131786– 131823. find
  48. Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. 2021. Informer: Beyond efficient transformer for long sequence time-series forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 35, pages 11106–11115. AAAI. find
  49. Tian Zhou, Peisong Niu, Liang Sun, Rong Jin, and 1 others. 2023. One fits all: Power general time series analysis by pretrained lm. Advances in neural information processing systems, 36:43322–43355. find

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