Comparative e-backtests for general risk measures
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908867694166016 |
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| author | Jiao, Zhanyi Wang, Qiuqi Zhao, Yimiao |
| author_facet | Jiao, Zhanyi Wang, Qiuqi Zhao, Yimiao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05840 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparative e-backtests for general risk measures Jiao, Zhanyi Wang, Qiuqi Zhao, Yimiao Methodology Econometrics Applications 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. |
| title | Comparative e-backtests for general risk measures |
| topic | Methodology Econometrics Applications |
| url | https://arxiv.org/abs/2511.05840 |