Hierarchical forecasting problems arise when time series have a natural group structure, and predictions at multiple levels of aggregation and disaggregation across the groups are needed. In such problems, it is often desired to satisfy the aggregation constraints in a given hierarchy, referred to as hierarchical coherence in the literature. Maintaining hierarchical coherence while producing accurate forecasts can be a challenging problem, especially in the case of probabilistic forecasting. We present a novel method capable of accurate and coherent probabilistic forecasts for hierarchical time series. We call it Deep Poisson Mixture Network (DPMN). It relies on the combination of neural networks and a statistical model for the joint distribution of the hierarchical multivariate time series structure. By construction, the model guarantees hierarchical coherence and provides simple rules for aggregation and disaggregation of the predictive distributions. We perform an extensive empirical evaluation comparing the DPMN to other state-of-the-art methods which produce hierarchically coherent probabilistic forecasts on multiple public datasets. Compared to existing coherent probabilistic models, we obtained a relative improvement in the overall Continuous Ranked Probability Score (CRPS) of 17.1% on Australian domestic tourism data, 24.2 on the Favorita grocery sales dataset, and 6.9% on a San Francisco Bay Area highway traffic dataset.

翻译：当时间序列具有自然的分组结构时,就会产生等级性预测问题,需要在各组之间进行多层次的汇总和分类预测。在这些问题中,通常希望它能够满足某个等级(即文献中的等级一致性)的总体限制,即文献中的等级一致性。保持等级一致性,同时作出准确的预测,可能是一个具有挑战性的问题,特别是在概率性预测的情况下。我们提出了一个新颖的方法,能够准确和一致地预测等级时间序列的概率性预测。我们称之为深皮松混合网络(DPMN),它依靠神经网络和统计模型的结合,共同分配等级性多变数时间序列结构。通过构建,模型保证等级一致性,并为预测性分布的汇总和分类提供简单规则。我们进行了广泛的实证评估,将DPMN与其他按等级一致地对多个公共数据集进行预测的可靠性预测。与现有的连贯的预测性模型相比,我们取得了相对改进,在澳大利亚国内旅游业数据17.1%的连续分级概率分数(CRPS)上,在旧金山销售数据上进行了广泛的实证评估。