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Proper Scoring Rules for Evaluating Density Forecasts with Asymmetric Loss Functions

posted on 11.03.2022, 20:00 authored by Matteo Iacopini, Francesco Ravazzolo, Luca Rossini

This article proposes a novel asymmetric continuous probabilistic score (ACPS) for evaluating and comparing density forecasts. It generalizes 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 (weighted) ACPS extends the symmetric (weighted) CRPS by allowing for asymmetries in the preferences underlying the scoring rule. A test is used to statistically compare the predictive ability of different forecasts. 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 in the ACPS are illustrated. Then, the proposed score and test are applied to assess and compare density forecasts of macroeconomic relevant datasets (U.S. employment growth) and of commodity prices (oil and electricity prices) with particular focus on the recent COVID-19 crisis period.


Matteo Iacopini acknowledges financial support from the EU Horizon 2020 programme under the Marie Skłodowska-Curie scheme (grant agreement no. 887220). Francesco Ravazzolo acknowledges financial support from Italian Ministry MIUR under the PRIN project “Hi-Di NET - Econometric Analysis of High Dimensional Models with Network Structures in Macroeconomics and Finance” (grant no. 2017TA7TYC).