Abstract: Identification and scoring functions are statistical tools to assess the calibration and the relative performance of risk measure estimates, e.g. in backtesting. A risk measure is called identifiable (elicitable) if it admits a strict identification function (strictly consistent scoring function). We consider measures of systemic risk introduced by Feinstein, Rudloff and Weber. Since these are set-valued, we work within the theoretical framework of Fissler, Frongillo, Hlavinová and Rudloff for forecast evaluation of set-valued functionals. We construct oriented selective identification functions, which induce a mixture representation of (strictly) consistent scoring functions. Their applicability is demonstrated with a simulation study.
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