🤖 AI Summary
Traditional conformal prediction relies on the exchangeability assumption, which fails in time series due to temporal dependence and distributional shift, undermining nominal coverage guarantees. To address this, we propose the first unified conformal prediction framework for non-exchangeable time series, establishing finite-sample theoretical guarantees for split conformal prediction under weak dependence conditions. We systematically categorize, model, and compare three mainstream strategies—reweighting, dynamic updating, and adaptive hyperparameter tuning—and integrate residual reweighting, online distribution calibration, and coverage-adaptive adjustment. Extensive experiments on diverse synthetic and real-world time series demonstrate that our method significantly narrows prediction intervals while strictly maintaining target coverage. Crucially, we quantitatively characterize the fundamental trade-off between interval width and predictive stability—the first such result—thereby providing both theoretical foundations and practical tools for reliable uncertainty quantification in nonstationary time series.
📝 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.