Combining forecasts from multiple temporal aggregation levels exploits information differences and mitigates model uncertainty, while reconciliation ensures a unified prediction that supports aligned decisions at different horizons. It can be challenging to estimate the full cross-covariance matrix for a temporal hierarchy, which can easily be of very large dimension, yet it is difficult to know a priori which part of the error structure is most important. To address these issues, we propose to use eigendecomposition for dimensionality reduction when reconciling forecasts to extract as much information as possible from the error structure given the data available. We evaluate the proposed estimator in a simulation study and demonstrate its usefulness through applications to short-term electricity load and financial volatility forecasting. We find that accuracy can be improved uniformly across all aggregation levels, as the estimator achieves state-of-the-art accuracy while being applicable to hierarchies of all sizes.

将来自多个时间聚合级别的预测组合起来可以利用信息差异并减轻模型的不确定性，而对帐则可以确保一个统一的预测，该预测可以支持不同水平的一致决策。估计时间层次的完整互协方差矩阵可能很困难，该矩阵很容易具有很大的维数，但是很难先验地知道误差结构的哪一部分是最重要的。为了解决这些问题，我们建议在调和预测时使用特征分解来降维，以在给定可用数据的情况下从错误结构中提取尽可能多的信息。我们在模拟研究中评估拟议的估算器，并通过将其应用于短期电力负荷和金融波动预测来证明其有用性。