Before revision:  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:  We describe corresponding comparative backtests of Diebold--Mariano type for superior systemic risk forecasts and comparable VaR forecasts, accompanied by a traffic-light approach .