Volatility-Corrected Prediction Intervals: Locally Adaptive Uncertainty Quantification for Probabilistic Time-Series Forecasting
Abstract
Prediction intervals from probabilistic time-series forecasters are commonly assessed by marginal coverage, the long-run proportion of observations falling inside the intervals. However, forecast errors in time series are often serially dependent and heteroskedastic, so prediction intervals can attain near-nominal marginal coverage while miscovering systematically during periods of larger local error variance. We identify and address this failure mode, which we call \emph{local scale miscalibration}. We first document the phenomenon using time-series foundation models (TSFMs): across several real-world series, their native intervals often attain near-nominal marginal coverage while exhibiting substantial temporal variation in local coverage, alternating between overcoverage and undercoverage over shorter windows. We then propose Volatility-Corrected Prediction Intervals (VCPI), a post-hoc calibration procedure that uses the base forecaster's predictive scale as a baseline, models the volatility of standardized forecast residuals with a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, and applies a multiplicative correction to produce locally adaptive prediction intervals. We justify VCPI both theoretically and empirically, comparing it against model-agnostic conformal counterparts. We provide a theoretical analysis of interval adaptation of the proposed method following abrupt changes in volatility. Empirically, we evaluate VCPI on Chronos, Moirai, and TimesFM across four real-world datasets and find that it produces more stable local coverage than conformal baselines while maintaining near-nominal marginal coverage and comparable interval width.
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BibTeX
@misc{cho2026volatilitycorrected,
title = {{Volatility-Corrected Prediction Intervals: Locally Adaptive Uncertainty Quantification for Probabilistic Time-Series Forecasting}},
author = {Jason B. Cho and David S. Matteson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31621},
eprint = {2610.31621},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31621},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Volatility-Corrected Prediction Intervals: Locally Adaptive Uncertainty Quantification for Probabilistic Time-Series Forecasting
AU - Jason B. Cho
AU - David S. Matteson
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31621
UR - https://arxiv.org/abs/2610.31621
AB - Prediction intervals from probabilistic time-series forecasters are commonly assessed by marginal coverage, the long-run proportion of observations falling inside the intervals. However, forecast errors in time series are often serially dependent and heteroskedastic, so prediction intervals can attain near-nominal marginal coverage while miscovering systematically during periods of larger local error variance. We identify and address this failure mode, which we call \emph{local scale miscalibration}. We first document the phenomenon using time-series foundation models (TSFMs): across several real-world series, their native intervals often attain near-nominal marginal coverage while exhibiting substantial temporal variation in local coverage, alternating between overcoverage and undercoverage over shorter windows. We then propose Volatility-Corrected Prediction Intervals (VCPI), a post-hoc calibration procedure that uses the base forecaster's predictive scale as a baseline, models the volatility of standardized forecast residuals with a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, and applies a multiplicative correction to produce locally adaptive prediction intervals. We justify VCPI both theoretically and empirically, comparing it against model-agnostic conformal counterparts. We provide a theoretical analysis of interval adaptation of the proposed method following abrupt changes in volatility. Empirically, we evaluate VCPI on Chronos, Moirai, and TimesFM across four real-world datasets and find that it produces more stable local coverage than conformal baselines while maintaining near-nominal marginal coverage and comparable interval width.
ER -