🤖 AI Summary
This work addresses the limitations of traditional conformal prediction, which relies on data exchangeability and struggles with non-exchangeable time series exhibiting seasonality, periodicity, or time-varying structures. The authors propose a spectral adaptive conformal prediction method that constructs weighted quantiles based on local spectral similarity and incorporates an online miscoverage rate calibration mechanism. This approach preserves finite-sample coverage guarantees while effectively capturing dynamic uncertainty in structured non-exchangeable data. By integrating spectral analysis, weighted conformal prediction, and effective sample size diagnostics, the method demonstrates superior performance over fixed spectral weighting strategies across simulations and three real-world U.S. datasets, confirming its robustness and reliability in handling complex temporal dependencies.
📝 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. We give an approximate coverage result for the fixed spectral weighted quantile and a deterministic long-run calibration result for the adaptive update. Simulations with recurring regimes and slowly changing frequencies, together with three U.S. real-data examples, show that the hybrid method can improve on fixed spectral weighting, while also showing that spectral weighting must be monitored through effective sample size diagnostics.