Conformal Prediction for Time Series with Deep Sequence Models

2026-10-01

AI Summary

This study addresses the failure of conformal prediction under non-exchangeable time series data and the lack of systematic investigation into deep learning models within this domain. To overcome these challenges, we propose three strategies, including conditional quantile regression, to systematically integrate deep sequence models such as RNNs and Transformers into the conformal prediction framework, further enhanced by localization techniques for improved adaptivity. We establish rigorous theoretical analyses demonstrating that asymptotic conditional coverage guarantees can be achieved under specific assumptions, thereby filling a critical theoretical gap in the literature. Extensive experiments on real-world datasets validate the effectiveness of the proposed methods, achieving time series forecasting that combines high predictive accuracy with reliable uncertainty quantification.

Abstract

Recent advances in deep learning for time series prediction have amplified the need for reliable uncertainty quantification. Conformal prediction has gained attention as a distribution-free framework for constructing prediction intervals with coverage guarantees. However, its coverage guarantees rely on data exchangeability, an assumption generally violated in time series. Active research has focused on developing conformal prediction methods for time series that overcome this limitation. While deep sequence models, such as recurrent neural networks and Transformers, have often been used in conformal prediction for time series, limited work has systematically studied how deep sequence models can be utilized in conformal prediction for time series. In this work, we systematically investigate the use of deep sequence models in conformal prediction for time series through three approaches: conditional quantile regression, conditional quantile function estimation, and localized conformal prediction. We provide a theoretical analysis establishing asymptotic conditional coverage guarantees for all three approaches under suitable assumptions. Through comprehensive experiments on real-world datasets, we demonstrate the effectiveness of leveraging deep sequence models into conformal prediction for time series.

Problem

• Conformal Prediction
• Time Series
• Deep Sequence Models
• Uncertainty Quantification
• Exchangeability

Innovation

• Conformal Prediction
• Time Series
• Deep Sequence Models
• Conditional Coverage
• Uncertainty Quantification