# Adaptive Conformal Inference for Multi-Step Ahead Time-Series Forecasting Online

arXiv: https://arxiv.org/abs/2409.14792 · HTML: https://mlsanity.com/paper/2409.14792/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 16 references that are in the map.
- First posted on arXiv 23 Sep 2024.

## Builds on (most cited first, 6 of 6)

- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [MAPIE: an open-source library for distribution-free uncertainty quantification](https://mlsanity.com/paper/2207.12274/) (2022)

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

- [KReF: Training-Free Retrieval for Long-Term Time-Series Forecasting and Predictive Uncertainty](https://mlsanity.com/paper/2608.06748/) (2026)
- [Adaptive Conformal Inference Under Delayed Feedback: Coverage Guarantees and a Delay-to-Memory Diagnostic](https://mlsanity.com/paper/2609.07251/) (2026)

## Abstract (arXiv)

The aim of this paper is to propose an adaptation of the well known adaptive conformal inference (ACI) algorithm to achieve finite-sample coverage guarantees in multi-step ahead time-series forecasting in the online setting. ACI dynamically adjusts significance levels, and comes with finite-sample guarantees on coverage, even for non-exchangeable data. Our multi-step ahead ACI procedure inherits these guarantees at each prediction step, as well as for the overall error rate. The multi-step ahead ACI algorithm can be used with different target error and learning rates at different prediction steps, which is illustrated in our numerical examples, where we employ a version of the confromalised ridge regression algorithm, adapted to multi-input multi-output forecasting. The examples serve to show how the method works in practice, illustrating the effect of variable target error and learning rates for different prediction steps, which suggests that a balance may be struck between efficiency (interval width) and coverage.t