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 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 time series when reliable hierarchical information is present. 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. Comparing to existing coherent probabilistic models, we obtain a relative improvement in the overall Continuous Ranked Probability Score (CRPS) of 11.8% on Australian domestic tourism data, and 8.1% on the Favorita grocery sales dataset, where time series are grouped with geographical hierarchies or travel intent hierarchies. For San Francisco Bay Area highway traffic, where the series' hierarchical structure is randomly assigned, and their correlations are less informative, our method does not show significant performance differences over statistical baselines.

翻译：当时间序列具有天然的分组结构，且需要跨组在多个聚合与分解层级上进行预测时，便会产生层次化预测问题。在此类问题中，通常需要满足给定层级结构中的聚合约束，即文献中所谓的"层次一致性"。在保持一致性的同时生成准确预测是一项具有挑战性的任务，尤其是在概率预测场景下。我们提出了一种新颖方法，能够在存在可靠层次信息的情况下，为时间序列提供准确且一致的层次化概率预测，并将其命名为深度泊松混合网络（DPMN）。该方法融合了神经网络与用于描述层级化多变量时间序列联合分布的统计模型。通过模型构建，该方法天然保证了层次一致性，并为预测分布的聚合与分解提供了简洁规则。我们进行了广泛的实证评估，将DPMN与多个公开数据集上产生层次一致概率预测的最先进方法进行了对比。与现有的一致性概率模型相比，在澳大利亚国内旅游数据上，整体连续排名概率评分（CRPS）相对提升了11.8%；在Favorita杂货销售数据集（其时间序列按地理层级或旅行意图层级分组）上，相对提升了8.1%。对于旧金山湾区高速公路交通数据（其序列的层次结构为随机分配，且序列间相关性信息量较低），我们的方法相较于统计基线并未表现出显著性能差异。