A Gentle Introduction to Conformal Time Series Forecasting

TL;DR

This paper reviews recent advances in conformal time series forecasting, addressing challenges of nonexchangeability, and compares methods for uncertainty quantification in dependent data.

Contribution

It unifies theoretical foundations and surveys state-of-the-art methods for conformal prediction in nonexchangeable time series data, including practical evaluation.

Findings

Finite-sample guarantees under weak dependence

Reweighting calibration data improves coverage

Trade-offs between coverage, width, and computational cost

Abstract

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.