# A Gentle Introduction to Conformal Time Series Forecasting

arXiv: https://arxiv.org/abs/2511.13608 · HTML: https://mlsanity.com/paper/2511.13608/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 40 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 19 of 19)

- [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)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [A Unified Comparative Study with Generalized Conformity Scores for Multi-Output Conformal Regression](https://mlsanity.com/paper/2501.10533/) (2025)
- [In-sample calibration yields conformal calibration guarantees](https://mlsanity.com/paper/2503.03841/) (2025)
- [Distribution-Free Prediction Bands for Multivariate Functional Time Series: an Application to the Italian Gas Market](https://mlsanity.com/paper/2107.00527/) (2021)
- [Conformal Prediction Bands for Two-Dimensional Functional Time Series](https://mlsanity.com/paper/2207.13656/) (2022)
- [Transformer Conformal Prediction for Time Series](https://mlsanity.com/paper/2406.05332/) (2024)

## Built on by (most cited first, 2 of 2)

- [Forecasting Multivariate Time Series under Predictive Heterogeneity: A Validation-Driven Clustering Framework](https://mlsanity.com/paper/2604.13748/) (2026)
- [Conformal bandits: bringing statistical validity and reward efficiency under weak arm separability](https://mlsanity.com/paper/2512.09850/) (2025)

## Abstract (arXiv)

Conformal prediction is a powerful post-hoc framework for uncertainty quantification that provides distribution-free coverage guarantees. However, these guarantees crucially rely on the assumption of exchangeability. This assumption is fundamentally violated in time series data, where temporal dependence and distributional shifts are pervasive. As a result, classical split-conformal methods may yield prediction intervals that fail to maintain nominal validity. This review unifies recent advances in conformal forecasting methods specifically designed to address nonexchangeable data. We first present a theoretical foundation, deriving finite-sample guarantees for split-conformal prediction under mild weak-dependence conditions. We then survey and classify state-of-the-art approaches that mitigate serial dependence by reweighting calibration data, dynamically updating residual distributions, or adaptively tuning target coverage levels in real time. Finally, we present a comprehensive simulation study that compares these techniques in terms of empirical coverage, interval width, and computational cost, highlighting practical trade-offs and open research directions.