Proper scoring rules for evaluating density forecasts with asymmetric loss functions

This article proposes a novel asymmetric continuous probabilistic score (ACPS) for evaluating and comparing density forecasts. It generalizes the proposed defines weighted version, which emphasizes regions of interest, such as tails or center variable’s range. The (weighted) ACPS extends symmetric CRPS by allowing asymmetries in preferences underlying scoring rule. A test is used to statistically compare predictive ability different general use any situation where decision-maker has evaluation In an artificial experiment, implications varying level asymmetry are illustrated. Then, applied assess forecasts macroeconomic relevant datasets (U.S. employment growth) commodity prices (oil electricity prices) with particular focus on recent COVID-19 crisis period.