Forecast combination and model averaging have become popular tools in forecasting and prediction, both of which combine a set of candidate estimates with certain weights and are often shown to outperform single estimates. A data-driven method to determine combination/averaging weights typically optimizes a criterion under certain weight constraints. While a large number of studies have been devoted to developing and comparing various weight choice criteria, the role of weight constraints on the properties of combination forecasts is relatively less understood, and the use of various constraints in practice is also rather arbitrary. In this study, we summarize prevalent weight constraints used in the literature, and theoretically and numerically compare how they influence the properties of the combined forecast. Our findings not only provide a comprehensive understanding on the role of various weight constraints but also practical guidance for empirical researchers how to choose relevant constraints based on prior information and targets.

翻译：预测组合与模型平均已成为预测领域广泛使用的工具，二者均通过特定权重整合一组候选估计值，并常被证明优于单一估计。确定组合/平均权重的数据驱动方法通常基于特定权重约束优化某一准则。尽管大量研究致力于开发与比较各类权重选择准则，但权重约束对组合预测性质的影响机制尚缺乏深入理解，且实践中各类约束的使用亦较为随意。本研究系统总结了文献中常见的权重约束，并从理论与数值模拟角度比较了它们如何影响组合预测的性质。我们的发现不仅深化了对各类权重约束作用的理解，还为实证研究者提供了基于先验信息与目标选择相关约束的实践指导。