A Gentle Introduction to Conformal Time Series Forecasting
M. Stocker, W. Małgorzewicz, M. Fontana, S. Ben Taieb
TL;DR
This paper surveys conformal forecasting for time series, focusing on non-exchangeable data. It classifies adaptive methods into four families (WCP, EnbPI, ACI, BCP) and provides a unified theoretical framework showing that standard split-conformal prediction remains approximately valid under weak dependence, while distribution shifts require adaptive strategies. Through simulation on AR, MA, mean-shift, and GARCH processes, it characterizes trade-offs in coverage, interval width, and computation, offering practical guidance for method selection. It also highlights open directions toward hybrid methods and distributional forecasting.
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.