Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting, where the goal is to model and forecast multivariate time-series that have underlying hierarchical relations. Most methods focus on point predictions and do not provide well-calibrated probabilistic forecasts distributions. Recent state-of-art probabilistic forecasting methods also impose hierarchical relations on point predictions and samples of distribution which does not account for coherency of forecast distributions. Previous works also silently assume that datasets are always consistent with given hierarchical relations and do not adapt to real-world datasets that show deviation from this assumption. We close both these gap and propose PROFHiT, which is a fully probabilistic hierarchical forecasting model that jointly models forecast distribution of entire hierarchy. PROFHiT uses a flexible probabilistic Bayesian approach and introduces a novel Distributional Coherency regularization to learn from hierarchical relations for entire forecast distribution that enables robust and calibrated forecasts as well as adapt to datasets of varying hierarchical consistency. On evaluating PROFHiT over wide range of datasets, we observed 41-88% better performance in accuracy and significantly better calibration. Due to modeling the coherency over full distribution, we observed that PROFHiT can robustly provide reliable forecasts even if up to 10% of input time-series data is missing where other methods' performance severely degrade by over 70%.

翻译：概率层次时间序列预测是时间序列预测的重要变体，其目标是对具有潜在层次关系的多元时间序列进行建模与预测。现有方法大多聚焦于点预测，无法提供校准良好的概率预测分布。最新概率预测方法虽将层次关系施加于点预测及分布样本上，却未能顾及预测分布的一致性。此外，既往研究默认数据集始终与给定层次关系保持一致，未针对真实数据集中偏离该假设的情况进行适配。我们同时弥补这两项不足，提出PROFHiT——一种全概率层次预测模型，可联合建模整个层次结构的预测分布。该模型采用灵活的概率贝叶斯方法，引入新颖的分布一致性正则化项，从层次关系中学习完整预测分布，从而实现鲁棒且校准良好的预测，并能适应层次一致性各异的数据集。在广泛的数据集上评估PROFHiT后，我们发现其准确率提升41-88%，且校准效果显著更优。由于对完整分布的一致性进行建模，即使输入时间序列数据缺失高达10%（其他方法性能严重下降逾70%），PROFHiT仍能稳健提供可靠预测。