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Tail Risk Inference via Expectiles in Heavy-Tailed Time Series

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  • Anthony C. Davison
  • Simone A. Padoan
  • Gilles Stupfler

Abstract

Expectiles define the only law-invariant, coherent and elicitable risk measure apart from the expectation. The popularity of expectile-based risk measures is steadily growing and their properties have been studied for independent data, but further results are needed to establish that extreme expectiles can be applied with the kind of dependent time series models relevant to finance. In this article we provide a basis for inference on extreme expectiles and expectile-based marginal expected shortfall in a general β-mixing context that encompasses ARMA and GARCH models with heavy-tailed innovations. Our methods allow the estimation of marginal (pertaining to the stationary distribution) and dynamic (conditional on the past) extreme expectile-based risk measures. Simulations and applications to financial returns show that the new estimators and confidence intervals greatly improve on existing ones when the data are dependent.

Suggested Citation

  • Anthony C. Davison & Simone A. Padoan & Gilles Stupfler, 2023. "Tail Risk Inference via Expectiles in Heavy-Tailed Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(3), pages 876-889, July.
    • Handle: RePEc:taf:jnlbes:v:41:y:2023:i:3:p:876-889
    DOI: 10.1080/07350015.2022.2078332
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    Cited by:

    1. Daouia, Abdelaati & Padoan, Simone A. & Stupfler, Gilles, 2024. "Extreme expectile estimation for short-tailed data," Journal of Econometrics, Elsevier, vol. 241(2).
    2. Zhang, Feipeng & Xu, Yixiong & Fan, Caiyun, 2023. "Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment," International Review of Financial Analysis, Elsevier, vol. 90(C).
    3. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Inference for extremal regression with dependent heavy-tailed data," TSE Working Papers 22-1324, Toulouse School of Economics (TSE), revised 29 Aug 2023.
    4. Abdelaati Daouia & Simone A. Padoan & Gilles Stupfler, 2024. "Extreme expectile estimation for short-tailed data," Post-Print hal-04672516, HAL.

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