Beschreibung
A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring functions are called strictly consistent for the functional. The elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores.In the first part of this talk, we explore the notion of higher order elicitability, that is, we investigate the question of elicitability for higher-dimensional functionals. As a result of particular applied interest we show that the pair (Value at Risk, Expected Shortfall) ((VaR, ES)) is elicitable despite the fact that ES itself is not. More generally, we give a characterization of the class of strictly consistent scoring functions for this pair, making use of a higher dimensional version of Osband's principle.
In the second part of the talk, we discuss the consequences of this result for backtesting ES-forecasts. We introduce comparative backtests of Diebold-Mariano type using a strictly consistent scoring function for the pair (VaR, ES). Comparative backtests open the possibility to choose a conservative null hypothesis in comparison to the current state of the art. Emphasizing our argument with a brief simulation study, we demonstrate that the change of the null hypothesis in comparative backtests amounts to a reversed onus of proof in backtesting decisions. This appears out to be beneficial to all stakeholders, including banks, regulators, and society at large.
| Zeitraum | 1 März 2016 → 4 März 2016 |
|---|---|
| Ereignistitel | 12th German Probability and Statistics Days |
| Veranstaltungstyp | Keine Angaben |
| Bekanntheitsgrad | International |