Before revision: In this article, we introduce a regression based backtest for the risk measure Expected Shortfall (ES) which is based on a joint regression framework for the quantile and the ES . We also introduce a second variant of this ES backtest which allows for testing one-sided hypotheses by only testing an intercept parameter.
After revision: In this article, we introduce a regression based backtest for the risk measure Expected Shortfall (ES) following the testing idea of Mincer and Zarnowitz (1969). Estimating a regression framework for the ES stand-alone is infeasible, and thus, our tests are based on a joint regression framework for the quantile and the ES . We also introduce a second variant of this ES backtest which allows for testing one-sided hypotheses by only testing an intercept parameter.