# Training-Free Probabilistic Time-Series Forecasting with Conformal Seasonal Pools

arXiv: https://arxiv.org/abs/2605.03789 · HTML: https://mlsanity.com/paper/2605.03789/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 12 of 12)

- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [ProbTS: Benchmarking Point and Distributional Forecasting across Diverse Prediction Horizons](https://mlsanity.com/paper/2310.07446/) (2023)
- [Computationally efficient versions of conformal predictive distributions](https://mlsanity.com/paper/1911.00941/) (2019)
- [Predictive inference for time series: why is split conformal effective despite temporal dependence?](https://mlsanity.com/paper/2510.02471/) (2025)
- [Conformal predictive distributions with kernels](https://mlsanity.com/paper/1710.08894/) (2017)

## Built on by (most cited first, 1 of 1)

- [Report the Floor: A Training-Free Conformal Interval Is a Mandatory Baseline for Probabilistic Time-Series Forecasting](https://mlsanity.com/paper/2606.09473/) (2026)

## Abstract (arXiv)

We propose Conformal Seasonal Pools (CSP), a training-free probabilistic time-series forecaster that mixes same-season empirical draws with signed residual draws around a seasonal naive forecast. In an audited rolling-origin benchmark on the six time-series datasets where DeepNPTS was originally evaluated (electricity, exchangerate, solarenergy, taxi, traffic, wikipedia), CSP-Adaptive significantly outperforms DeepNPTS on every metric we report -- CRPS (per-window paired Wilcoxon p ≈ 4 × 10-10), normalized mean quantile loss (p ≈ 7 × 10-10), and empirical 95% coverage (p ≈ 8 × 10-45, mean 0.89 vs 0.66) -- while running over 500x faster on CPU. Coverage is the most decision-critical of these: a 0.95 nominal interval that contains the truth in only ~66% of cases fails the basic calibration desideratum and would not survive deployment in safety- or decision-critical settings. The failure mode is also more severe than aggregate coverage suggests: in the worst 10% of windows, DeepNPTS's prediction interval covers none of the H forecast horizons -- the entire multi-step trajectory misses the truth at every step simultaneously. This poses serious risk in safety- and decision-critical applications such as healthcare, finance, energy operations, and autonomous systems, where prediction intervals that systematically miss the truth across the entire planning horizon translate directly into misclassified patients, regulatory capital failures, grid imbalances, and safety-case violations. CSP achieves all of this with no learned parameters and no training. We argue training-free conformal samplers should be mandatory baselines when evaluating learned non-parametric forecasters.