# Adaptive Conformal Predictions for Time Series

arXiv: https://arxiv.org/abs/2202.07282 · HTML: https://mlsanity.com/paper/2202.07282/

## Key facts

- Cited by 161 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 14 of 14)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [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)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [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)
- [Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark](https://mlsanity.com/paper/2008.08004/) (2020)
- [A Second-order Bound with Excess Losses](https://mlsanity.com/paper/1402.2044/) (2014)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Optimal learning with Bernstein Online Aggregation](https://mlsanity.com/paper/1404.1356/) (2014)
- [CRPS Learning](https://mlsanity.com/paper/2102.00968/) (2021)
- [Conformal Prediction Interval Estimations with an Application to Day-Ahead and Intraday Power Markets](https://mlsanity.com/paper/1905.07886/) (2019)
- [Expert Aggregation for Financial Forecasting](https://mlsanity.com/paper/2111.15365/) (2021)

## Built on by (most cited first, 30 of 161)

- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (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)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions](https://mlsanity.com/paper/2310.05921/) (2023)
- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [High-Dimensional Prediction for Sequential Decision Making](https://mlsanity.com/paper/2310.17651/) (2023)
- [Achieving Risk Control in Online Learning Settings](https://mlsanity.com/paper/2205.09095/) (2022)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Conformal Prediction Sets Improve Human Decision Making](https://mlsanity.com/paper/2401.13744/) (2024)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Distribution Free Prediction Sets for Node Classification](https://mlsanity.com/paper/2211.14555/) (2022)
- [C-RAG: Certified Generation Risks for Retrieval-Augmented Language Models](https://mlsanity.com/paper/2402.03181/) (2024)
- [Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)](https://mlsanity.com/paper/2405.06627/) (2024)
- [Conformal Prediction with Temporal Quantile Adjustments](https://mlsanity.com/paper/2205.09940/) (2022)
- [Conformal Prediction with Missing Values](https://mlsanity.com/paper/2306.02732/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Split Localized Conformal Prediction](https://mlsanity.com/paper/2206.13092/) (2022)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Forking Uncertainties: Reliable Prediction and Model Predictive Control with Sequence Models via Conformal Risk Control](https://mlsanity.com/paper/2310.10299/) (2023)
- [Deep learning models for price forecasting of financial time series: A review of recent advancements: 2020-2022](https://mlsanity.com/paper/2305.04811/) (2023)
- [Localized Adaptive Risk Control](https://mlsanity.com/paper/2405.07976/) (2024)

## Abstract (arXiv)

Uncertainty quantification of predictive models is crucial in decision-making problems. Conformal prediction is a general and theoretically sound answer. However, it requires exchangeable data, excluding time series. While recent works tackled this issue, we argue that Adaptive Conformal Inference (ACI, Gibbs and Cand`es, 2021), developed for distribution-shift time series, is a good procedure for time series with general dependency. We theoretically analyse the impact of the learning rate on its efficiency in the exchangeable and auto-regressive case. We propose a parameter-free method, AgACI, that adaptively builds upon ACI based on online expert aggregation. We lead extensive fair simulations against competing methods that advocate for ACI's use in time series. We conduct a real case study: electricity price forecasting. The proposed aggregation algorithm provides efficient prediction intervals for day-ahead forecasting. All the code and data to reproduce the experiments is made available.