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Backtesting Systemic Risk Forecasts Using Multi-Objective Elicitability

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  • Tobias Fissler
  • Yannick Hoga

Abstract

Systemic risk measures such as CoVaR, CoES, and MES are widely-used in finance, macroeconomics and by regulatory bodies. Despite their importance, we show that they fail to be elicitable and identifiable. This renders forecast comparison and validation, commonly summarized as “backtesting,” impossible. The novel notion of multi-objective elicitability solves this problem by relying on bivariate scores equipped with the lexicographic order. Based on this concept, we propose Diebold–Mariano type tests with suitable bivariate scores to compare systemic risk forecasts. We illustrate the test decisions by an easy-to-apply traffic-light approach. Finally, we apply our traffic-light approach to DAX 30 and S&P 500 returns, and infer some recommendations for regulators.

Suggested Citation

  • Tobias Fissler & Yannick Hoga, 2024. "Backtesting Systemic Risk Forecasts Using Multi-Objective Elicitability," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(2), pages 485-498, April.
    • Handle: RePEc:taf:jnlbes:v:42:y:2024:i:2:p:485-498
    DOI: 10.1080/07350015.2023.2200514
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    Citations

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    Cited by:

    1. Tobias Fissler & Yannick Hoga, 2024. "How to Compare Copula Forecasts?," Papers 2410.04165, arXiv.org.
    2. Sullivan Hu'e & Christophe Hurlin & Yang Lu, 2024. "Backtesting Expected Shortfall: Accounting for both duration and severity with bivariate orthogonal polynomials," Papers 2405.02012, arXiv.org, revised May 2024.
    3. Timo Dimitriadis & Marius Puke, 2026. "Statistical Inference for Score Decompositions," Papers 2603.04275, arXiv.org.
    4. Timo Dimitriadis & Yannick Hoga, 2026. "Systemic Risk Surveillance," Papers 2601.08598, arXiv.org.
    5. Laura Garcia‐Jorcano & Lidia Sanchis‐Marco, 2025. "Measuring the Impact of Transition Risk on Financial Markets: A Joint VaR‐ES Approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 44(6), pages 1907-1945, September.
    6. Yannick Hoga & Christian Schulz, 2025. "Self-Normalized Inference in (Quantile, Expected Shortfall) Regressions for Time Series," Papers 2502.10065, arXiv.org, revised Jun 2025.
    7. Koike, Takaaki & Chen, Cathy W.S. & Lin, Edward M.H., 2025. "Forecasting and backtesting gradient allocations of expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 124(C).

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