Combining Many Forecasts with General Loss Functions

经济时间序列往往难以预测，因此不同的预测者在面对预测同一经济变量时，往往会得出截然不同的答案，这反映出他们使用了不同的预测模型、信息集和估计方法。个别预测系统地支配其他预测是非常罕见的。许多研究发现，简单的等权重预测组合比单个模型产生的预测更好。该项目开发了理论工具和经验技术，以解释为什么简单的等权重预测在实践中如此有效，并将其与更广泛类别的组合进行比较。本研究项目开发了可与等权预测组合相竞争的估算与预测组合方法。我们建立了一些条件，在这些条件下，我们提出的方法可以产生改进的预测。研究项目还考虑了不同预测组合方法在多种经济环境下的表现，包括对近期、中期和远期经济变量的预测，对经济变量的整个概率分布的预测，以及为个别决策者或经济决策者量身定制的损失函数预测。该提案还研究了让预测组合权重随时间变化的可能性，因为一些模型可能在某些情况下（例如，当经济处于衰退状态时）工作得更好，而另一些模型可能在不同的情况下（例如，膨胀状态）表现得更好。预报组合技术已被发现在实际情况中是有用的。本建议提供了对为什么会这样的进一步理解，并在理论上和实践中探索了各种替代方法，特别是当涉及许多预测时，并以新的方式扩展了方法。开发这些方法的兴趣在一定程度上是由首席调查员的实际关切所驱动的，这些关切是通过与各联邦储备银行和其他国际组织（如国际货币基金组织）的互动，以及通过考虑他们的需求和要求而产生的。我们期望在赠款期间继续与这些组织和其他组织保持牢固的关系。

Economic time series are often difficult to predict and as a result different forecasters, faced with predicting the same economic variable, often come up with very different answers, reflecting their use of separate forecasting models, information sets and estimation methods. It is very rare for any individual forecast to systematically dominate the others. Many studies have found that a simple equal-weighted combination of forecasts produces better predictions than those generated by individual models. This project develops both theoretical tools and empirical techniques for explaining why simple equal-weighted forecasts do so well in practice and compares these with wider classes of combinations. The research project develops estimation and forecast combination methods that can compete with the equal-weighted forecast combination. We establish conditions under which our proposed methods can be expected to produce improved forecast. The research project also considers the performance of different forecast combination methods under a host of economic circumstances, including prediction of economic variables in the near, medium and distant future, prediction of the entire probability distribution of an economic variable and prediction with loss functions that are tailored to individual policy makers or economic decision makers. The proposal also investigates the possibility of letting the forecast combination weights vary over time since some models may work better in some situations (e.g. when the economy is in a recession) and others may prove to be better in different circumstances (e.g. an expansion state). Forecast combination techniques have already been found to be useful in practical situations. This proposal provides further understanding of why this is so and explores various alternative approaches both theoretically and in practice, particularly when many forecasts are involved, and expands the approach in new ways. The interest in developing these methods is in part driven by practical concerns of the Principal Investigators that has come through interaction with the various Federal Reserve banks and other international organizations such as the IMF and through considering their needs and requests. We expect to continue strong relations with these and other organizations through the grant period.