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. These two backtests are the first backtests in the literature which solely backtest the risk measure ES as they only require ES forecasts as input parameters.
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 framework for the quantile and the ES . We also introduce a second variant of this ES backtest which allows for different test specifications. These ES backtests are the first backtests in the literature which solely backtest the risk measure ES as they only require ES forecasts as input parameters.