Drift-Aware Spectral Conformal Prediction for Non-Exchangeable Streaming Data

Abstract: Conformal prediction provides distribution-free prediction intervals under exchangeability, but many modern data streams are neither independent nor stable. They exhibit recurring regimes, changing seasonal frequencies, abrupt shifts, and gradual drift. We propose drift-aware spectral conformal prediction (DASC), a streaming uncertainty quantification framework for structured non-exchangeable data subject to distributional drift. DASC forms conformal prediction intervals using calibration residuals weighted by local spectral similarity, while a transport-based drift score monitors whether the current test distribution has moved away from past calibration regimes. When drift is mild, DASC borrows calibration residuals from structurally similar historical windows; when drift is severe, it contracts or reweights the calibration pool and updates the target miscoverage level online. The method also reports an effective sample size diagnostic that warns when a weighted conformal quantile is statistically fragile. We establish an approximate coverage bound that decomposes coverage loss into drift, residual mismatch, and weighted effective sample size. In synthetic experiments and five stress-test regimes, DASC maintains near-nominal coverage after drift where rolling, recency-weighted, and spectral-only conformal methods can under-cover. In real electricity and weather streams, DASC reduces average interval width by approximately 28% and 42%, respectively, relative to the best calibrated non-DASC baseline, while preserving calibrated or conservative coverage. A financial volatility example shows a more nuanced regime in which spectral-only calibration is competitive, but DASC retains near-nominal coverage and adds drift diagnostics.