This paper proposes a novel asymmetric continuous probabilistic score (ACPS) for evaluating and comparing density forecasts. It extends the proposed score and defines a weighted version, which emphasizes regions of interest, such as the tails or the center of a variable's range. The ACPS is of general use in any situation where the decision maker has asymmetric preferences in the evaluation of the forecasts. In an artificial experiment, the implications of varying the level of asymmetry are illustrated. Then, the proposed score is applied to assess and compare density forecasts of macroeconomic relevant datasets (unemployment rate) and of commodity prices (oil and electricity prices) with a particular focus on the recent COVID crisis period.
Proper scoring rules for evaluating asymmetry in density forecasting