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This paper introduces a novel method for generating reliable prediction intervals in time-series data that exhibit complex, non-exchangeable structures like seasonality and shifting regimes. By leveraging spectral similarity to weight calibration residuals dynamically, the approach maintains finite-sample coverage guarantees even when standard assumptions of independence or stationarity are violated. The theoretical framework provides explicit bounds on error decomposition while demonstrating practical improvements over existing adaptive baselines in real-world economic datasets.
Spectral Adaptive Conformal Prediction for Structured Non-Exchangeable Data
arXiv:2606.15950v2 Announce Type: replace-cross Abstract: Conformal prediction gives prediction intervals with finite-sample coverage when the data are exchangeable. Many time-indexed datasets are not exchangeable: they have seasons, recurring regimes, changing frequencies, or other forms of structured dependence. This paper studies a simple way to use that structure. We propose spectral adaptive conformal prediction, a method that forms weighted conformal quantiles using local spectral similarity and then updates the target miscoverage level online. The spectral weights choose calibration residuals that look relevant to the current test point. The adaptive update corrects the long-run miss rate when uncertainty changes over time. The theory makes both parts controllable. We give an approximate coverage bound that splits the error into a spectral mismatch term and an effective-sample-size term, prove that kernel spectral weighting never increases the mismatch term relative to uniform weighting, show that a bandwidth of order N^(-1/(d+2)) balances the two terms, and establish an unconditional long-run calibration bound for the adaptive update that holds for every sample path without independence or stationarity. Simulations with recurring regimes and slowly changing frequencies, together with four real-data examples spanning monthly, weekly, and daily U.S. and European series, show when the hybrid method improves on strong adaptive baselines and when it does not, and an effective-sample-size safeguard, computable at prediction time without outcomes, detects and repairs the one observed failure.
Abstract:Conformal prediction gives prediction intervals with finite-sample coverage when the data are exchangeable. Many time-indexed datasets are not exchangeable: they have seasons, recurring regimes, changing frequencies, or other forms of structured dependence. This paper studies a simple way to use that structure. We propose spectral adaptive conformal prediction, a method that forms weighted conformal quantiles using local spectral similarity and then updates the target miscoverage level online. The spectral weights choose calibration residuals that look relevant to the current test point. The adaptive update corrects the long-run miss rate when uncertainty changes over time. The theory makes both parts controllable. We give an approximate coverage bound that splits the error into a spectral mismatch term and an effective-sample-size term, prove that kernel spectral weighting never increases the mismatch term relative to uniform weighting, show that a bandwidth of order N^(-1/(d+2)) balances the two terms, and establish an unconditional long-run calibration bound for the adaptive update that holds for every sample path without independence or stationarity. Simulations with recurring regimes and slowly changing frequencies, together with four real-data examples spanning monthly, weekly, and daily U.S. and European series, show when the hybrid method improves on strong adaptive baselines and when it does not, and an effective-sample-size safeguard, computable at prediction time without outcomes, detects and repairs the one observed failure.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2606.15950 [stat.ML]
(or arXiv:2606.15950v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2606.15950 Focus to learn more arXiv-issued DOI via DataCite
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