Optimal reconciliation with immutable forecasts

TL;DR

This paper introduces a novel hierarchical forecast reconciliation method that allows certain forecasts to remain unchanged, ensuring unbiasedness and applicability to grouped hierarchies, with demonstrated empirical benefits.

Contribution

It proposes a new reconciliation approach that maintains immutable forecasts, applicable across different hierarchy levels and groups, while preserving unbiasedness and accounting for error correlations.

Findings

Method preserves unbiasedness of base forecasts.

Applicable to grouped hierarchies with immutable variables.

Empirical results show improved forecast accuracy in retail data.

Abstract

The practical importance of coherent forecasts in hierarchical forecasting has inspired many studies on forecast reconciliation. Under this approach, so-called 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, in general, 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 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 non-negativity of forecasts. We also perform empirical experiments, including an application to sales of a large scale online retailer, to assess the impacts of our proposed methodology.