Hierarchical time series are common in several applied fields. Forecasts 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：在几个应用领域,等级时间序列很常见。 预测需要一致, 也就是说, 满足等级的制约。 最受欢迎的执行一致性的技术是调和, 即调和, 调整每个时间序列计算的基础预测。 然而, 最近关于概率调和的工作有几个限制。 在本文中, 我们提出一种新的方法, 以调和任何类型的预测分布的条件为基础。 然后我们引入一种新的算法, 叫做自下而上的重要性抽样, 以便从调和的分布中有效地取样。 它可以用于任何基础预测分布: 离散、 连续或以样本的形式, 提供与当前方法相比的重大加速。 一些时间等级的实验显示比基准概率预测有显著的改进 。