# SGA: Uncertainty Quantification for Multi-Step Forecasting in Time Series Foundation Models

arXiv: https://arxiv.org/abs/2609.28582 · HTML: https://mlsanity.com/paper/2609.28582/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 21 of 21)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Unsupervised Quality Estimation for Neural Machine Translation](https://mlsanity.com/paper/2005.10608/) (2020)
- [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)
- [Bias-Reduced Uncertainty Estimation for Deep Neural Classifiers](https://mlsanity.com/paper/1805.08206/) (2018)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [Aurora: Towards Universal Generative Multimodal Time Series Forecasting](https://mlsanity.com/paper/2509.22295/) (2025)
- [Timer-S1: A Billion-Scale Time Series Foundation Model with Serial Scaling](https://mlsanity.com/paper/2603.04791/) (2026)
- [Financial Fine-tuning a Large Time Series Model](https://mlsanity.com/paper/2412.09880/) (2024)
- [Beyond Accuracy: Are Time Series Foundation Models Well-Calibrated?](https://mlsanity.com/paper/2510.16060/) (2025)
- [ProbFM: Probabilistic Time Series Foundation Model with Uncertainty Decomposition](https://mlsanity.com/paper/2601.10591/) (2026)
- [When to Trust, How to Distill: Multi-Foundation Model Guidance for Lightweight, Robust Scientific Time Series Forecasting](https://mlsanity.com/paper/2606.19363/) (2026)

## Abstract (arXiv)

The recent emergence of Time Series Foundation Models (TSFMs) has significantly advanced multi-step forecasting performance, enabling accurate predictions over extended future horizons. However, existing TSFMs often suffer from significantly inherent uncertainty, which typically manifests as derived forecast branches emerging at each time step and spreading to subsequent steps; different forecast branches often exhibit varying forecasting performance, thereby undermining the credibility of TSFM forecasts. In this paper, we propose the Slicing-Graphing-Alignment (SGA) method to quantify the uncertainty of multi-step TSFM forecasts. The proposed SGA first characterizes the topology of all potential forecast branches using a directed acyclic graph, such that the graph complexity bounds the uncertainty of multi-step forecasts, and then precisely measures the graph complexity by integrating both topological information and TSFM-inherent stochasticity. Experimental results conducted on 11 TSFMs and 27 datasets demonstrate that (i) SGA achieves the best performance when ranking predictive errors with uncertainty estimates; (ii) SGA works with a more extensive and more precise sampling coverage than those of existing UQ methods, deriving a quantification mechanism fundamentally different from those of established ones; and (iii) larger model scales of TSFMs correlate with lower uncertainty estimates of multi-step forecasts, suggesting another empirical scaling law for uncertainty quantification of multi-step TSFM forecasts.