From Recoverability to Functional Use: Certifying Temporal Reports in Time-Series Forecasting
Authors: Qipeng Qian, Yuntao Qian
Organizations: SUPCON Technology, Hangzhou, China · College of Artificial Intelligence, Zhejiang University, Hangzhou 310027, China
Abstract
Temporal reports are increasingly emitted alongside numerical forecasts and are often interpreted as statements about the computation producing those forecasts. We formalize the resulting certification problem as three distinct stages: \emph{recoverability}, \emph{report correctness}, and \emph{functional use}. For point delays, an exact finite-sample recovery--substitutability identity ties structural discrimination and proxy prediction to the same realized shift geometry while placing them on different scales: structural evidence grows with nηn, whereas the normalized predictive penalty is governed by ηn. A delay can therefore be statistically decisive while an alternative lag remains near-oracle. Guided by this regime, we evaluate TCN- and N-HiTS-based systems on the strict intersection of recoverable trajectories, correct reports, and near-oracle one-step predictions. Their dominant forecast dependence remains far from the reported delay under masking, finite perturbations, local Jacobians, and in-distribution conditional replacement, and the separation persists across a 100-fold forecast-loss sweep. A no-bypass factorization then provides an explicit access certificate for the final stage, while architecture-matched multi-seed, post-hoc, and gate-destruction controls identify report-coordinate access as the mechanism governing alignment. The resulting framework separates statistical evidence for \emph{what can be identified} from computational evidence for \emph{what the forecast uses}.
Forecasting leaderboards rank models by predictive quality, but their winners are often read as deployment-ready top-1 advice. That reading can fail when forecasts are passed through a fixed decision interface, such as an alert threshold, a top-k budget, or a switching-cost policy. We study when a forecast-side winner can be certified as deployment-actionable for a specified interface and deployed utility. We introduce a fail-closed certification protocol whose gates are sufficient evidential conditions for a strong claim: a friction-caused, non-tie, statistically supported, and recurrent deployment-side reversal. Traffic-Hourly provides a certified anchor: winners agree at zero friction, but positive switching friction makes the forecast winner deployed-suboptimal. A locked native audit tests overclaiming: across 22 verified candidates and 362 full-grid cells, 155 apparent forecast/deployment winner inversions are blocked before certification. The contribution is not a new forecaster, metric, or universal utility, but a conservative protocol for deciding when forecasting leaderboard winners should be read as deployment-actionable top-1 advice.
Conformal prediction (CP) provides distribution-free prediction intervals for fixed forecasters, but its standard calibration procedure is often inefficient for time series data, where forecast errors are temporally dependent and change across time and operating conditions. Recent time series CP methods improve local calibration using recent, weighted, or localized residuals. Yet local calibration can remain indirect, since broad residual weighting or additional adaptation procedures may dilute the evidence most relevant to the current prediction. This motivates a simple retrieval and correction strategy that selects similar past residuals as local evidence and then corrects the coverage error left by retrieval. In this paper, we propose Retrieval--Corrected Conformal Prediction (RCCP), a retrieval-augmented calibration method for time series prediction intervals. RCCP builds an asymmetric interval from retrieved one-sided residuals and calibrates its normalized retrieval error with a scalar conformal correction. Thus, retrieval provides local residual evidence, while conformal correction determines the final scale needed for coverage. We provide a coverage-gap bound based on the stability of the normalized retrieval error distribution. Across standard benchmarks and backbone forecasters, RCCP attains the target coverage in every setting and achieves the lowest Winkler scores, with fewer severe misses. RCCP also achieves low calibration and inference overhead, showing that retrieval-corrected calibration is an effective and scalable approach to uncertainty quantification in time series forecasting. Code is available at https://github.com/jinsaaang/rccp.
Forecasting systems in science must be accurate, physically consistent, and certifiably reliable. Most existing models address prediction, constraint enforcement, and verification separately, limiting scalability and interpretability. We introduce GeoCert, a geometric AI framework that unifies forecasting, physical reasoning, and formal verification within a single differentiable computation. GeoCert formulates forecasting as evolution along a hyperbolic manifold, where negative curvature induces contraction dynamics, intrinsic robustness, and logarithmic-time certification. A hierarchical constraint architecture separates universal physical laws from domain-specific dynamics, enabling certified generalization across energy, climate, finance, and transportation systems. GeoCert achieves state-of-the-art accuracy while reducing computational cost by 97.5% and maintaining better certification rates. By embedding verification into the geometry of learning, GeoCert transforms forecasting from empirical approximation to formally verified inference, offering a scalable foundation for trustworthy, reproducible, and physically grounded scientific AI.