arXiv:2606.15950 · v3
Spectral Similarity Weights for Adaptive Conformal Prediction: A Bias-Variance Account and a Benchmark
摘要
Conformal prediction intervals lose their guarantee when a series is not exchangeable. We study weighting calibration residuals by the similarity of local Fourier power features, combined with the adaptive level update of ACI. A two-term account of the coverage error, mismatch that falls and sampling error that rises as the bandwidth shrinks, holds with exogenous features and conditionally independent residuals, but not for features computed from the series itself, which is how the method is used. In four simulations, spectral weighting lowered the mean regime-level deviation of coverage by 17% to 19% when the features came from the response and by 75% when they were exogenous, and not clearly under gradual drift. In each recurring-regime design a scaled-error baseline or Conformal PID control calibrated better. On nine public series with 36 forecast origins, spectral weighting with the plain weighted quantile did not differ from projected ACI in coverage error, and Conformal PID and scaled ACI were the best calibrated methods. The features are blind to seasonal phase, so the weights act like a recency kernel. A pure recency kernel did at least as well, especially with a finite-sample rank correction (mean absolute coverage error 0.039 against 0.090 for ACI; a post hoc check). Calendar phase weights narrowed German electricity intervals by 23% at equal coverage, but were not better than ACI across the series. We suggest trying adaptive baselines first, and similarity weights only where regimes differ in spectral shape or season and the effective sample size stays large.
作者备注：28 pages plus a 9-page supplement (ancillary file). Revised version that supersedes v2. Code and results: https://github.com/jopoku16/spectral-similarity-conformal