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.

翻译：时间序列常呈现可加性层次结构。在此类结构中，高层级时间序列是其下属序列的加总。这种层次结构对预测结果施加了自然约束，但传统的单变量预测技术无法保证这种预测一致性。一种直接解决方案是仅对底层序列进行预测，并通过聚合得到高层级预测值，该方法即经典的"自下而上"预测法。在开创性研究中，\citep{Wickramasuriya2019}提出了名为MinT的最优协调方法，其核心目标是最小化所有预测误差协方差矩阵的迹。MinT算法在预测性能上已证明优于自下而上及其他传统方法，因而获得广泛应用。本文通过模拟实验研究了MinT在极短时间序列与大规模层次结构场景下的表现，该场景使MinT所需的协方差估计变得尤为困难。我们提出了一种创新的迭代方法，能显著减少待估参数数量，从而进一步提升预测精度。最后，基于世界半导体贸易统计组织（WSTS）提供的权威半导体市场数据，通过半导体数据集案例研究展示了MinTit方法的具体应用。