Reconciliation enforces coherence between hierarchical forecasts, in order to satisfy a set of linear constraints. While most works focus on the reconciliation of point forecasts, we consider probabilistic reconciliation and we analyze the properties of distributions reconciled via conditioning. We provide a formal analysis of the variance of the reconciled distribution, treating the case of Gaussian and count forecasts separately. We also study the reconciled upper mean in the case of one-level hierarchies, again treating Gaussian and count forecasts separately. We then show experiments on the reconciliation of intermittent time series related to the count of extreme market events. The experiments confirm our theoretical results and show that reconciliation largely improves the performance of probabilistic forecasting.

协调可强制分层预测之间的一致性，以满足一组线性约束。虽然大多数工作都集中在点预测的协调上，但我们考虑概率协调并分析通过条件协调的分布的属性。我们对协调分布的方差进行正式分析，分别处理高斯和计数预测的情况。我们还研究了一级层次结构情况下的协调上均值，再次分别处理高斯预测和计数预测。然后，我们展示了与极端市场事件计数相关的间歇时间序列的协调实验。实验证实了我们的理论结果，并表明协调极大地提高了概率预测的性能。