具有鲁棒性的分层时间序列预测
Hierarchical Time Series Forecasting with Robust Reconciliation
AI总结：
本文提出了一种鲁棒优化框架，用于分层时间序列预测中的不确定性调整，以提升预测性能。
摘要：
本文聚焦于预测分层时间序列数据，其中每个高层观测值等于其对应低层时间序列之和。在这种情况下，预测值应保持一致，即每个父系列的预测值应恰好等于其子系列预测值之和。现有的分层预测方法通常为每个系列独立生成基础预测，然后应用一种调整程序以使结果在层次结构中保持一致。这些方法通常通过预测误差的协方差矩阵来推导最优的调整。然而，在实践中，真实的协方差矩阵是未知的，必须从有限样本中进行估计。真实协方差矩阵与估计协方差矩阵之间的差距可能会降低预测性能。为了解决这个问题，我们提出了一种用于分层调整的鲁棒优化框架，该框架考虑了估计协方差矩阵的不确定性。我们首先引入一个不确定性集用于估计协方差矩阵，并提出一个调整问题，该问题最小化该不确定性集上加权平方残差的最坏情况平均值。我们证明我们的问题是可以通过半正定优化问题来解决的。数值实验表明，所提出的鲁棒调整方法在预测性能上优于现有的分层预测方法，这表明将不确定性整合到调整过程中是有效的。
英文摘要：
This paper focuses on forecasting hierarchical time-series data, where each higher-level observation equals the sum of its corresponding lower-level time series. In such contexts, the forecast values should be coherent, meaning that the forecast value of each parent series exactly matches the sum of the forecast values of its child series. Existing hierarchical forecasting methods typically generate base forecasts independently for each series and then apply a reconciliation procedure to adjust them so that the resulting forecast values are coherent across the hierarchy. These methods generally derive an optimal reconciliation, using a covariance matrix of the forecast error. In practice, however, the true covariance matrix is unknown and has to be estimated from finite samples in advance. This gap between the true and estimated covariance matrix may degrade forecast performance. To address this issue, we propose a robust optimization framework for hierarchical reconciliation that accounts for uncertainty in the estimated covariance matrix. We first introduce an uncertainty set for the estimated covariance matrix and formulate a reconciliation problem that minimizes the worst-case average of weighted squared residuals over this uncertainty set. We show that our problem can be cast as a semidefinite optimization problem. Numerical experiments demonstrate that the proposed robust reconciliation method achieved better forecast performance than existing hierarchical forecasting methods, which indicates the effectiveness of integrating uncertainty into the reconciliation process.
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。
