This paper presents a formal framework and proposes algorithms to extend forecast reconciliation to discrete-valued data, including low counts. A novel method is introduced based on recasting the optimisation of scoring rules as an assignment problem, which is solved using quadratic programming. The proposed framework produces coherent joint probabilistic forecasts for count hierarchical time series. Two discrete reconciliation algorithms are also proposed and compared against generalisations of the top-down and bottom-up approaches for count data. Two simulation experiments and two empirical examples are conducted to validate that the proposed reconciliation algorithms improve forecast accuracy. The empirical applications are forecasting criminal offences in Washington D.C. and product unit sales in the M5 dataset. Compared to benchmarks, the proposed framework shows superior performance in both simulations and empirical studies.

中文翻译：

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离散预测调节


本文提出了一个正式的框架，并提出了将预测协调扩展到离散值数据（包括低计数）的算法。引入了一种基于将评分规则优化重新定义为分配问题的新方法，该问题使用二次规划来解决。所提出的框架为计数分层时间序列产生一致的联合概率预测。还提出了两种离散协调算法，并将其与计数数据的自上而下和自下而上方法的概括进行比较。进行了两个仿真实验和两个实证例子来验证所提出的协调算法提高了预测精度。实证应用是预测华盛顿特区的刑事犯罪和 M5 数据集中的产品单位销量。与基准相比，所提出的框架在模拟和实证研究中都显示出优越的性能。