通过聚类构建层次时间序列：是否存在一种最优的预测方式？
Constructing hierarchical time series through clustering: Is there an optimal way for forecasting?
AI总结：
本文研究预测协调中层次结构的构建方式，通过比较多种时间序列聚类表示与距离定义、随机置换实验及跨层次预测平均，发现准确性提升主要来自层次结构而非相似序列分组，且多方法平均表现最佳。
摘要：
近年来，预测协调（forecast reconciliation）引起了显著的研究兴趣，但大多数研究都将时间序列的层次结构视为既定条件。我们扩展了利用时间序列聚类构建层次结构的现有工作，以提高预测准确性为目标，并从三个方面进行了拓展。首先，我们研究了多种聚类方法，不仅包括不同的聚类算法，还包括时间序列的表示方式以及时间序列之间距离的定义方式。我们发现，相对于两层层次结构，基于聚类的层次结构能够带来预测准确性的提升。其次，我们设计了一种基于层次结构随机置换的方法，在保持层次结构固定的同时，将时间序列随机分配到各个聚类中。由此我们发现，使用聚类所带来的预测准确性提升并非源于将相似序列分组在一起，而是源于层次结构本身。第三，我们提出了一种对使用不同聚类方法构建的多个层次结构的预测结果进行平均的方法，结果表明该方法优于任何单一聚类方法。所有分析均在两个基准数据集和一个模拟数据集上进行。我们的发现为层次结构构建在预测协调中的作用提供了新的见解，并为预测实践提供了有价值的指导。
英文摘要：
Forecast reconciliation has attracted significant research interest in recent years, with most studies taking the hierarchy of time series as given. We extend existing work that uses time series clustering to construct hierarchies, with the goal of improving forecast accuracy, in three ways. First, we investigate multiple approaches to clustering, including not only different clustering algorithms, but also the way time series are represented and how distance between time series is defined. We find that cluster-based hierarchies lead to improvements in forecast accuracy relative to two-level hierarchies. Second, we devise an approach based on random permutation of hierarchies, keeping the structure of the hierarchy fixed, while time series are randomly allocated to clusters. In doing so, we find that improvements in forecast accuracy that accrue from using clustering do not arise from grouping together similar series but from the structure of the hierarchy. Third, we propose an approach based on averaging forecasts across hierarchies constructed using different clustering methods, that is shown to outperform any single clustering method. All analysis is carried out on two benchmark datasets and a simulated dataset. Our findings provide new insights into the role of hierarchy construction in forecast reconciliation and offer valuable guidance on forecasting practice.
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