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 in Feinstein et al. (Measures of systemic risk. SIAM J. Financial Math. 8:672-708, 2017). Since these are set-valued, we work within the theoretical framework of Fissler et al. (Forecast evaluation of set-valued functionals. Preprint, 2020) 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 comprehensive simulation study.