Title: Encompassing tests for higher-order elicitable functionals
Authors: Julie Schnaitmann - Universität Konstanz (Germany) [presenting]
Timo Dimitriadis - Heidelberg Institute for Theoretical Studies (Germany)
Abstract: Encompassing tests are introduced for forecasts of higher-order elicitable functionals such as the variance and the Expected Shortfall (ES). Encompassing tests rely on the existence of strictly consistent loss functions for the forecasted functionals under consideration, which do not exist for the variance and the ES. However, for these functionals, such loss functions exist for the pairs (mean, variance) and (quantile, ES). We utilize these joint loss functions in order to introduce joint encompassing tests for the quantile and the ES as well as stand-alone encompassing tests for the ES. These tests provide a theoretical justification for forecast combination of the ES when encompassing is rejected. We show through simulation studies that all the proposed tests are reasonably sized and exhibit good power properties against general alternatives in typical financial applications. In the empirical application, we apply encompassing tests in order to demonstrate the superiority of forecast combination methods for the ES.