Hierarchical time series are common in several applied fields. The forecasts for these time series are required to be coherent, that is, to satisfy the constraints given by the hierarchy. The most popular technique to enforce coherence is called reconciliation, which adjusts the base forecasts computed for each time series. However, recent works on probabilistic reconciliation present several limitations. In this paper, we propose a new approach based on conditioning to reconcile any type of forecast distribution. We then introduce a new algorithm, called Bottom-Up Importance Sampling, to efficiently sample from the reconciled distribution. It can be used for any base forecast distribution: discrete, continuous, or in the form of samples, providing a major speedup compared to the current methods. Experiments on several temporal hierarchies show a significant improvement over base probabilistic forecasts.

翻译：层级时间序列在多个应用领域中普遍存在。这些时间序列的预测需满足一致性要求，即必须符合层级结构所施加的约束条件。实现一致性的最常用技术称为协同预测，它通过调整各时间序列的基础预测值来达成目标。然而，近期关于概率协同预测的研究存在若干局限性。本文提出一种基于条件概率的新方法，可协同任意类型的预测分布。进而引入新算法——自底向上重要性采样，用于高效地从协同分布中生成样本。该方法适用于离散型、连续型或样本形式的任意基础预测分布，相较于现有方法能显著提升计算速度。基于多个时间层级的实验表明，本方法相较于基础概率预测取得了显著改进。