Point forecasts can be interpreted as functionals (i.e., point summaries) of predictive distributions. We extend methodology for the identification of the functional based on time series of point forecasts and associated realizations. Focusing on state-dependent quantiles and expectiles, we provide a generalized method of moments estimator for the functional, along with tests of optimality under general joint hypotheses of functional relationships and information bases. Our tests are more flexible, and in simulations better calibrated and more powerful than existing solutions. In empirical examples, economic growth forecasts and model output for precipitation are indicative of overstatement in anticipation of extreme events.

中文翻译：

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用未知指令解释点预测

点预测可以解释为预测分布的函数（即点汇总）。我们扩展了基于点预测和相关实现的时间序列来识别功能的方法。专注于状态相关的分位数和期望值，我们提供了泛函矩估计器的广义方法，以及在函数关系和信息库的一般联合假设下的最优性测试。我们的测试更灵活，在模拟中比现有解决方案校准得更好，功能更强大。在实证示例中，降水的经济增长预测和模型输出表明对极端事件的预测被夸大了。