This talk is concerned with set-valued functionals, e.g., quantiles, the expected region of a flood, or systemic risk measures introduced in . We introduce a thorough distinction between selective forecasts, specifying single points in the set of interest, and exhaustive forecasts, describing the entire set. This induces two corresponding types of elicitability and identifiability, which turn out to be mutually exclusive . We construct selective identification functions and exhaustive scoring functions for systemic risk measures studied in . In a simulation study, we consider comparative backtests of Diebold-Mariano type as well as Murphy diagrams.
23 Sep. 2019 → 26 Sep. 2019
Jahrestagung der Deutschen Mathematischen Vereinigung