Nonlinear Probabilistic Forecast Reconciliation

TL;DR

This paper introduces the first methods for probabilistic forecast reconciliation with nonlinear constraints, extending existing linear techniques using projection and UKF-inspired sampling, with empirical validation showing improved accuracy.

Contribution

It develops and compares two novel approaches for nonlinear probabilistic forecast reconciliation, a previously unaddressed problem in the field.

Findings

Both methods improve forecast accuracy.

UKF-based approach is faster and performs best overall.

Methods validated on synthetic and real datasets.

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.