Before revision:  In particular, we prove that conditional elicitability of two functionals implies joint multi-objective elicitability with respect to the lexicographic order on \mathbb{R}^2 , which makes it applicable in the context of CoVaR, MES or (CoVaR, CoES), together with VaR. We describe corresponding comparative backtests of Diebold-Mariano type , for two-sided and 'one and a half'-sided hypotheses, which respect the particularities of the lexicographic order and which can be used in a regulatory setting .
After revision:  In particular, we prove that conditional elicitability of two functionals implies joint multi-objective elicitability with respect to the lexicographic order on \mathbb{R}^2 . We establish comparative backtests of Diebold-Mariano type , for two-sided and 'one and a half'-sided hypotheses, which respect the particularities of the lexicographic order and which can be used in a regulatory setting .