# Conformal Prediction Algorithms for Time Series Forecasting: Methods and Benchmarking

arXiv: https://arxiv.org/abs/2601.18509 · HTML: https://mlsanity.com/paper/2601.18509/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 18 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 11 of 11)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (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 PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [Online conformal inference for multi-step time series forecasting](https://mlsanity.com/paper/2410.13115/) (2024)
- [Coverage-Guaranteed Prediction Sets for Out-of-Distribution Data](https://mlsanity.com/paper/2403.19950/) (2024)

## Abstract (arXiv)

Reliable uncertainty quantification is of critical importance in time series forecasting, yet traditional methods often rely on restrictive distributional assumptions. Conformal prediction (CP) has emerged as a promising distribution-free framework for generating prediction intervals with rigorous theoretical guarantees. However, applying CP to sequential data presents a primary challenge: the temporal dependencies inherent in time series fundamentally violate the core assumption of data exchangeability, upon which standard CP guarantees are built. This paper critically examines the main categories of algorithmic solutions designed to address this conflict. We survey and benchmark methods that relax the exchangeability assumption, those that redefine the data unit to be a collection of independent time series, approaches that explicitly model the dynamics of the prediction residuals, and online learning algorithms that adapt to distribution shifts to maintain long-run coverage. We use AutoARIMA as the base forecaster on a large-scale monthly sales dataset, evaluating marginal coverage, interval width, and the Winkler score. Our benchmark results show that multi-step split conformal prediction method meets the 90% coverage threshold and demonstrates the best efficiency.