These Matlab codes compute 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. The folder contains two main scripts that implement a GARCH(1,1) model and a AR(1)-GARCH(1,1) model, respectively. To compute the backtests, the user must choose the number p of risk levels, and the coverage level tau of ES. The scripts are applied to the daily returns of the S&P500 index over the period 1997-2012 and allow to reproduce most of the figures and tables of the empirical application of this article.
Journal of Risk and Insurance (2021)
Fritzsch Simon and Scharner Philipp