Diebold-Mariano and model confidence set tests have low power and high type III error rates when comparing extreme quantile VaR and ES forecasts on short out-of-sample windows.
To illustrate how correlations affect the MCS test, assume that we compare only two models i and j and that the variances are fixed
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Evaluating financial tail risk forecasts: Testing Equal Predictive Ability
Diebold-Mariano and model confidence set tests have low power and high type III error rates when comparing extreme quantile VaR and ES forecasts on short out-of-sample windows.