Interpretation of point forecasts with unknown directive

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.