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.

翻译：预测协调调整独立生成的预测，使其满足某些已知约束。虽然概率预测协调在线性约束下已相当成熟，但某些实际预测问题涉及变量间的非线性关系。本文首次研究了具有非线性约束的概率预测协调方法。我们将基于投影和条件化这两种协调方法扩展到非线性约束情形。投影方法通过将预测样本映射到非线性相干流形上来实现协调。条件化方法则采用受无迹卡尔曼滤波（UKF）启发的采样算法。我们基于合成数据集和真实数据集对两种方法进行了评估。实验表明，两种协调方法普遍能提升预测准确性。基于UKF的方法在实现最佳整体性能的同时，其运行速度显著快于投影方法。