Comparing Predictive Accuracy in the Presence of a Loss Function Shape Parameter

We develop tests for out-of-sample forecast comparisons based on loss functions that contain shape parameters. Examples include using average utility across a range of values the level risk aversion, accuracy characteristics portfolio return weight vector, and recently-proposed “Murphy diagrams” classes consistent scoring rules. An extensive Monte Carlo study verifies our have good size power properties in realistic sample sizes, particularly when compared with existing methods which break down then number considered parameter grows. present three empirical illustrations new test.