The practical importance of coherent forecasts in hierarchical forecasting has inspired many studies on forecast reconciliation. Under this approach, base forecasts are produced for every series in the hierarchy and are subsequently adjusted to be coherent in a second reconciliation step. Reconciliation methods have been shown to improve forecast accuracy but will generally adjust the base forecast of every series. However, in an operational context, it is sometimes necessary or beneficial to keep forecasts of some variables unchanged after forecast reconciliation. In this paper, we formulate a reconciliation methodology that keeps forecasts of a pre-specified subset of variables unchanged or “immutable”. In contrast to existing approaches, these immutable forecasts need not all come from the same level of a hierarchy, and our method can also be applied to grouped hierarchies. We prove that our approach preserves unbiasedness in base forecasts. Our method can also account for correlations between base forecasting errors and ensure the non-negativity of forecasts. We also perform empirical experiments, including an application to a large-scale online retailer’s sales, to assess our proposed methodology’s impacts.

相干预测在分层预测中的实际重要性激发了许多关于预测协调的研究。在这种方法下，为层次结构中的每个系列生成基础预测，并随后在第二个协调步骤中进行调整以保持一致。协调方法已被证明可以提高预测的准确性，但通常会调整每个系列的基础预测。然而，在操作环境中，有时在预测核对后保持某些变量的预测不变是必要的或有益的。在本文中，我们制定了一种协调方法，使预先指定的变量子集的预测保持不变或“不可变”。与现有方法相比，这些不可变的预测不需要全部来自同一层级，我们的方法也可以应用于分组层次结构。我们证明我们的方法在基础预测中保持无偏见。我们的方法还可以解释基本预测误差之间的相关性并确保预测的非负性。我们还进行了实证实验，包括应用于大型在线零售商的销售，以评估我们提出的方法的影响。