Coherence is not enough: Aggregation constraints across predictive distributions, forecasts and decisions

2026-09-14

AI Summary

论文探讨了不同聚合层次预测的一致性问题，分析了在预测分布、汇总统计和决策中应用约束的差异，并提出了确保一致性的方法。

Abstract

Forecasts made at different levels of aggregation are often required to agree---for example, regional forecasts should sum to the national total. Forecast reconciliation imposes such relationships, but the meaning of agreement depends on whether the constraint is applied to a predictive distribution, a reported summary such as a mean or quantile, or a decision based on the forecast. We show that these operations are not interchangeable. Even when every possible outcome from a predictive distribution satisfies an aggregation rule, its separately reported marginal quantiles need not add up; under nonlinear relationships, even the coordinatewise means may violate the constraint. We characterise when linear reconciliation preserves marginal quantiles and show that nonmedian quantiles generally cannot be preserved in a genuine hierarchy. We also explain why conditioning on an exact nonlinear constraint requires specifying how that constraint is observed or approximated, and identify when the predictive mean contains enough information for a constrained decision. In an application to Australian tourism data with 28 rolling forecast origins, the median discrepancy between two natural constructions of the national 95th percentile is 159.9\% of the reconciled 90\% prediction-interval width under bottom-up reconciliation. Rankings of mean- and quantile-based forecasts also reverse when squared-error loss is replaced by asymmetric inventory loss. These results provide a framework for deciding what should be made coherent and how competing methods should be evaluated.

Problem

• forecast reconciliation
• aggregation constraints
• predictive distribution
• marginal quantiles
• decision making

Innovation

• forecast reconciliation
• aggregation constraints
• predictive distribution
• quantile preservation
• nonlinear constraint