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Hierarchical forecasting problems arise when time series have a natural groupstructure, and predictions at multiple levels of aggregation and disaggregationacross the groups are needed. In such problems, it is often desired to satisfythe aggregation constraints in a given hierarchy, referred to as hierarchicalcoherence in the literature. Maintaining coherence while producing accurateforecasts can be a challenging problem, especially in the case of probabilisticforecasting. We present a novel method capable of accurate and coherentprobabilistic forecasts for time series when reliable hierarchical informationis present. We call it Deep Poisson Mixture Network (DPMN). It relies on thecombination of neural networks and a statistical model for the jointdistribution of the hierarchical multivariate time series structure. Byconstruction, the model guarantees hierarchical coherence and provides simplerules for aggregation and disaggregation of the predictive distributions. Weperform an extensive empirical evaluation comparing the DPMN to otherstate-of-the-art methods which produce hierarchically coherent probabilisticforecasts on multiple public datasets. Comparing to existing coherentprobabilistic models, we obtain a relative improvement in the overallContinuous Ranked Probability Score (CRPS) of 11.8% on Australian domestictourism data, and 8.1% on the Favorita grocery sales dataset, where time seriesare grouped with geographical hierarchies or travel intent hierarchies. For SanFrancisco Bay Area highway traffic, where the series' hierarchical structure israndomly assigned, and their correlations are less informative, our method doesnot show significant performance differences over statistical baselines.

Probabilistic Hierarchical Forecasting with Deep Poisson Mixtures