Backtesting risk measures is a central task in financial regulation. While standard backtests evaluate whether a forecasting model is statistically consistent with observed losses, regulatory practice often requires assessing the performance of an internal model relative to benchmark models. We develop a non-parametric sequential framework for comparative backtests of general elicitable risk measures using e-values and e-processes. The proposed methods provide anytime-valid inference and remain robust under dependence and model misspecification. In particular, we propose a modified three-zone approach based on weak dominance, which yields more informative conclusions in comparative backtesting. As a technical building block, we also construct general standard e-backtests for identifiable risk measures and characterize the associated e-values and e-processes. The resulting procedures apply to a broad class of commonly used risk measures, including the mean, variance, Value-at-Risk, Expected Shortfall, and expectiles. Simulation studies and empirical analyses illustrate the effectiveness of the proposed approach.

翻译：回测风险度量是金融监管的核心任务。标准回测评估预测模型在统计上是否与观测损失一致，而监管实践通常要求评估内部模型相对于基准模型的表现。我们利用e值和e过程，为一般可引出风险度量的比较回测开发了一个非参数序贯框架。所提方法提供任意时间有效的推断，并在依赖性和模型设定错误下保持稳健。特别地，我们提出了一种基于弱优势的改进三区方法，该方法在比较回测中能得出更具信息量的结论。作为技术构建模块，我们还为可识别风险度量构建了一般标准e-回测，并刻画了相关的e值和e过程。所得程序适用于一大类常用风险度量，包括均值、方差、风险价值、期望缺口和期望分位数。模拟研究和实证分析说明了所提方法的有效性。