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) which is based on a joint regression for the Value at Risk 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.