Proper Scoring Rules for Evaluating Density Forecasts with Asymmetric Loss Functions
提出一种非对称连续概率评分（ACPS）来评估和比较密度预测，允许评分规则中的偏好不对称，并通过实验和实际数据（美国就业增长、石油和电力价格）验证其有效性，特别关注COVID-19危机时期。
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.