Comparing Possibly Misspecified Forecasts
通过分析和模拟表明，当预测模型存在设定错误、参数估计误差或信息集不嵌套时，不同一致损失函数对预测的排序会不同，因此评估者应指定单一的损失函数。
Recent work has emphasized the importance of evaluating estimates of a statistical functional (such as a conditional mean, quantile, or distribution) using a loss function that is consistent for the functional of interest, of which there is an infinite number. If forecasters all use correctly specified models free from estimation error, and if the information sets of competing forecasters are nested, then the ranking induced by a single consistent loss function is sufficient for the ranking by any consistent loss function. This article shows, via analytical results and realistic simulation-based analyses, that the presence of misspecified models, parameter estimation error, or nonnested information sets, leads generally to sensitivity to the choice of (consistent) loss function. Thus, rather than merely specifying the target functional, which narrows the set of relevant loss functions only to the <i>class</i> of loss functions consistent for that functional, forecast consumers or survey designers should specify the single specific loss function that will be used to evaluate forecasts. An application to survey forecasts of U.S. inflation illustrates the results.