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.
International Journal of Research in Marketing (2019)
Gaustad Tarje, M. Bendik, Warlop Luk, and Fitzsimons Gavan J.