Description
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. 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. The elicitability of the pair (VaR, ES) leads the way to comparative backtests of Diebold-Marianotype. Moreover, we discuss the choice of a ‘good’ scoring function. While strict consistency is commonly undoubted to be a minimal requirement of a ‘good’ scoring function, we introduce further appealing properties that should be satisfied, such as homogeneity, convexity or order-sensitivity of scoring functions. These results should give guidance in the choice of a scoring function in general, and in particular for the pair (Value at Risk, Expected Shortfall).| Period | 15 Feb 2017 → 17 Feb 2017 |
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| Event title | Workshop on Risk Quantification and Extreme Values in Applications |
| Event type | Unknown |
| Degree of Recognition | International |