Nonlinear Probabilistic Forecast Reconciliation

2026-04-29

AI Summary

This study addresses the limitation of existing probabilistic forecast reconciliation methods, which are restricted to linear constraints and struggle to capture nonlinear relationships among variables. The work extends probabilistic forecast reconciliation to scenarios involving nonlinear constraints by proposing two general-purpose frameworks: one employs a projection-based approach to map predictive samples onto a nonlinearly consistent manifold, while the other introduces a conditional sampling strategy inspired by the unscented Kalman filter (UKF), leveraging the unscented transform. Empirical evaluations on both synthetic and real-world datasets demonstrate that both methods substantially improve forecast accuracy, with the UKF-based approach consistently achieving superior performance and significantly higher computational efficiency compared to the projection method.

Abstract

Forecast reconciliation adjusts independently generated forecasts so that they satisfy some known constraints. While probabilistic forecast reconciliation is well established for linear constraints, some practical forecasting problems involve nonlinear relationships among variables. In this paper, we address probabilistic forecast reconciliation with nonlinear constraints for the first time. We extend both reconciliation via projection and conditioning to the case of nonlinear constraints. The projection approach reconciles forecast samples by mapping them onto the nonlinear coherent manifold. The conditioning approach adopts a sampling algorithm inspired to the Unscented Kalman Filter (UKF). We evaluate both methods on synthetic and real datasets. Empirically, both reconciliation approaches generally improve forecast accuracy. The UKF-based approach achieves the best overall performance while being substantially faster than the projection one.

Problem

• probabilistic forecast reconciliation
• nonlinear constraints
• forecast coherence
• nonlinear relationships

Innovation

• nonlinear forecast reconciliation
• probabilistic forecasting
• Unscented Kalman Filter
• coherent manifold
• forecast conditioning