A Gentle Introduction to Conformal Time Series Forecasting
It tackles the problem of uncertainty quantification in time series forecasting for researchers and practitioners, but it is incremental as it reviews and classifies existing advances rather than introducing new methods.
This review addresses the challenge of applying conformal prediction to time series data, where exchangeability assumptions are violated, by unifying recent methods that adapt to temporal dependence and distributional shifts, and it includes a simulation study comparing empirical coverage, interval width, and computational cost.
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.