We propose forecast encompassing tests for the Expected Shortfall (ES) jointly with the Value at Risk (VaR) based on flexible link (or combination) functions. Our setup allows testing encompassing for convex forecast combinations and for link functions which preclude crossings of the combined...

Rational respondents to economic surveys may report as a point forecast any measure of the central tendency of their (possibly latent) predictive distribution, for example the mean, median, mode, or any convex combination thereof. We propose tests of forecast rationality when the measure of...