This Matlab code computes the four regression-based backtests for ES of the article "Backtesting Expected Shortfall via Multi-Quantile Regression". The test statistics are devised to assess the coefficients of a multi-quantile regression model which satisfy specific properties when the ES forecasts are valid. To compute the backtests, users must choose the number p of risk levels, and the coverage level tau of ES. The script is applied to the daily returns of the S&P500 index over the period 1997-2012 and allows users to reproduce the figures and tables of the empirical application of this article.
Working Paper (2018)