Forecast encompassing tests and probability forecasts
针对概率预测提出预测包含检验，使用二次和对数评分规则，推导检验统计量的极限分布并考察参数估计的影响，通过衰退概率预测和调查概率预测实例展示其应用。
Abstract We consider tests of forecast encompassing for probability forecasts, for both quadratic and logarithmic scoring rules. We propose test statistics for the null of forecast encompassing, present the limiting distributions of the test statistics, and investigate the impact of estimating the forecasting models' parameters on these distributions. The small‐sample performance is investigated, in terms of small numbers of forecasts and model estimation sample sizes. We show the usefulness of the tests for the evaluation of recession probability forecasts from logit models with different leading indicators as explanatory variables, and for evaluating survey‐based probability forecasts. Copyright © 2009 John Wiley & Sons, Ltd.