EVALUATING DENSITY FORECASTS

Abstract

We propose methods for evaluating and improving density forecasts.We focus primarily on methods that are applicable regardless of the particular user's loss function, though we take explicit account of the relationships between density forecasts, action choices, and the corresponding expected loss throughout.We illustrate the methods with a detailed series of examples, and we discuss extensions to improving and combining suboptimal density forecasts, multistep-ahead density forecast evaluation, multivariate density forecast evaluation, monitoring for structural change and its relationship to density forecasting, and density forecast evaluation with known loss function.