Backtesting expected shortfall and beyond
研究了多种预期损失回测方法的表现，比较了它们在分析复杂度、模型稳定性、样本量敏感性和计算负担上的差异，发现传统方法可能失效，而基于VaR-ES联合可评分函数的测试在模型比较中有优势。
We conduct a comprehensive study of the performance of leading backtesting procedures for expected shortfall. The tests differ in their analytical complexity, stability over different models, sensitivity to the sample sizes (both estimation and backtesting), and computational burden. The best performing scenario depends on the interaction between estimation error and backtesting error. We document that the speed of convergence to the nominal size also varies across tests. Traditional tests may fail to validate the candidate model, in which case we show that a scoring function test based on the joint elicitability of VaR-ES may have merit from a model comparison perspective.