用于极短层级时间序列调和的迭代迹最小化方法
Iterative Trace Minimization for the Reconciliation of Very Short Hierarchical Time Series
AI总结：
针对极短且层级较大的时间序列中 MinT 协方差估计困难的问题，提出减少待估参数的迭代迹最小化方法，并通过模拟与 WSTS 半导体案例验证其预测精度提升。
摘要：
时间序列通常以加法层级结构出现。在这种情况下，较高层级的时间序列是其下属时间序列之和。这种层级结构对预测施加了天然约束。然而，单变量预测技术无法确保这种预测一致性。一个显而易见的解决方案是仅预测底层时间序列，并通过聚合获得较高层级的预测。这种方法也被称为自下而上方法。在其开创性论文中，Wickramasuriya 等人（2019）提出了一种名为 MinT 的最优调和方法。该方法试图最小化所有预测误差的基础协方差矩阵的迹。MinT 算法已展现出优于自下而上方法及其他方法的性能，并广受欢迎。本文提供了一项模拟研究，考察 MinT 在极短时间序列和较大层级结构下的性能。这种情形使 MinT 所需的协方差估计变得困难。文中引入了一种新颖的迭代方法，可显著减少待估参数的数量。该方法能够进一步提高预测精度。文中还借助一个半导体数据集的案例研究展示了 MinTit 的应用，该数据集基于世界半导体贸易统计组织（WSTS）提供的数据；WSTS 是一家领先的半导体市场数据提供商。
英文摘要：
Time series often appear in an additive hierarchical structure. In such cases, time series on higher levels are the sums of their subordinate time series. This hierarchical structure places a natural constraint on forecasts. However, univariate forecasting techniques are incapable of ensuring this forecast coherence. An obvious solution is to forecast only bottom time series and obtain higher level forecasts through aggregation. This approach is also known as the bottom-up approach. In their seminal paper, \citep{Wickramasuriya2019} propose an optimal reconciliation approach named MinT. It tries to minimize the trace of the underlying covariance matrix of all forecast errors. The MinT algorithm has demonstrated superior performance to the bottom-up and other approaches and enjoys great popularity. This paper provides a simulation study examining the performance of MinT for very short time series and larger hierarchical structures. This scenario makes the covariance estimation required by MinT difficult. A novel iterative approach is introduced which significantly reduces the number of estimated parameters. This approach is capable of improving forecast accuracy further. The application of MinTit is also demonstrated with a case study at the hand of a semiconductor dataset based on data provided by the World Semiconductor Trade Statistics (WSTS), a premier provider of semiconductor market data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
