Optimal probabilistic forecasts: When do they work?

Proper scoring rules are used to assess the out-of-sample accuracy of probabilistic forecasts, with different rewarding distinct aspects forecast performance. Herein, we re-investigate practice using proper produce forecasts that ‘optimal’ according a given score and when their is superior alternative score. Particular attention paid relative predictive performance under misspecification model. Using numerical illustrations, document several novel findings within this paradigm highlight important interplay between true data generating process, assumed model rule. Notably, show only sufficiently compatible process allow particular criterion reward what it designed reward, will approach forecasting reap benefits. Subject compatibility, however, superiority optimal be greater, greater degree misspecification. We explore these issues range scenarios both artificially simulated empirical data.