# When the Martingale Never Stops Firing: Anytime-Valid Gating on Real Forecast Streams

arXiv: https://arxiv.org/abs/2608.30502 · HTML: https://mlsanity.com/paper/2608.30502/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 17 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Builds on (most cited first, 10 of 10)

- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [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)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning](https://mlsanity.com/paper/2505.23719/) (2025)
- [Testing exchangeability: fork-convexity, supermartingales, and e-processes](https://mlsanity.com/paper/2102.00630/) (2021)
- [Retrain or not retrain: Conformal test martingales for change-point detection](https://mlsanity.com/paper/2102.10439/) (2021)
- [E-detectors: a nonparametric framework for sequential change detection](https://mlsanity.com/paper/2203.03532/) (2022)
- [Combining Evidence Across Filtrations](https://mlsanity.com/paper/2402.09698/) (2024)

## Abstract (arXiv)

Machine learning systems are increasingly corrected while they run, and the decision of when to intervene is increasingly delegated to statistical monitors. Anytime-valid inference promises evidence that can be acted on at any moment, exactly the guarantee this setting needs, and it is moving from theory into deployed monitoring. Conformal test martingales are the change-detection instrument, and Ville's inequality caps their false-alarm probability on exchangeable data. The guarantee is conditional. A deployment inherits it only if the stream it monitors behaves exchangeably. The premise is hardest to satisfy where these monitors are most useful, on dependent data and inside loops where the monitor modifies the learner whose scores it reads. It is also rarely measured. We measure it in a pre-specified case study, where such a monitor gates the online updates of a Kalman adapter correcting frozen time-series foundation models on five forecasting streams. On exchangeable synthetic streams, the same implementation fires in at most 1 of 60 runs. On the real streams, at alpha = 0.05, 135 of 135 clean-stream runs fired. The construction does not explain the firing; the failure comes from the deployed score stream itself. Repeated fires hold the gate's drift response active, and the gated filter amplifies the very transient it was designed to prevent. The component worth keeping makes no validity claim. Huber-style gating of the filter's own updates cuts isolated-spike degradation by an order of magnitude with no dataset specific tuning. Anytime-valid methods proposed for dependent data should therefore be accompanied by null-calibration controls and mechanism traces.