Efficient conformal prediction intervals for time series: Online PID-Expert aggregation
Abstract
For a given point forecaster, proportional-integral-derivative (PID) calibration configurations can attain similar overall coverage yet produce different interval widths. We introduce PID-Expert, an online aggregation method for improving the efficiency of conformal prediction intervals for time series. PID-Expert combines thresholds from a fixed library of PID calibrators, each evolving under its own coverage feedback. Aggregation weights depend on normalized interval width and miscoverage, while a shared multiplier adapts the miscoverage penalty using feedback from the reported interval. We establish local regret bounds for weighted expert losses under the realized multiplier sequence and, separately, a pathwise upper bound on time-averaged aggregate miscoverage, with control in expectation and almost surely under a stability condition. Across four simulation settings and two real-data applications, PID-Expert produces narrower mean intervals than a prespecified Conformal PID benchmark while keeping overall empirical coverage close to the nominal level. Compared with expert selection and equal averaging, aggregation generally provides a more balanced coverage--width trade-off across forecasting settings. Rolling analyses further reveal local coverage--efficiency trade-offs, particularly following abrupt distributional shifts. Overall, PID-Expert reduces reliance on a single PID configuration while improving interval efficiency.
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BibTeX
@misc{liu2026efficient,
title = {{Efficient conformal prediction intervals for time series: Online PID-Expert aggregation}},
author = {Guodong Liu and Yanfei Kang and Ren Miao and Xiaoqian Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02777},
eprint = {2610.02777},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02777},
}
RIS
TY - UNPB
TI - Efficient conformal prediction intervals for time series: Online PID-Expert aggregation
AU - Guodong Liu
AU - Yanfei Kang
AU - Ren Miao
AU - Xiaoqian Wang
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02777
UR - https://arxiv.org/abs/2610.02777
AB - For a given point forecaster, proportional-integral-derivative (PID) calibration configurations can attain similar overall coverage yet produce different interval widths. We introduce PID-Expert, an online aggregation method for improving the efficiency of conformal prediction intervals for time series. PID-Expert combines thresholds from a fixed library of PID calibrators, each evolving under its own coverage feedback. Aggregation weights depend on normalized interval width and miscoverage, while a shared multiplier adapts the miscoverage penalty using feedback from the reported interval. We establish local regret bounds for weighted expert losses under the realized multiplier sequence and, separately, a pathwise upper bound on time-averaged aggregate miscoverage, with control in expectation and almost surely under a stability condition. Across four simulation settings and two real-data applications, PID-Expert produces narrower mean intervals than a prespecified Conformal PID benchmark while keeping overall empirical coverage close to the nominal level. Compared with expert selection and equal averaging, aggregation generally provides a more balanced coverage--width trade-off across forecasting settings. Rolling analyses further reveal local coverage--efficiency trade-offs, particularly following abrupt distributional shifts. Overall, PID-Expert reduces reliance on a single PID configuration while improving interval efficiency.
ER -