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Nonparametric estimation of expected shortfall for α-mixing financial losses

Author

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  • Xuejun Wang

    (Anhui University)

  • Yi Wu

    (Chizhou University)

  • Wei Wang

    (Chizhou University)

Abstract

In this paper, we investigate the Bahadur type representation of a nonparametric expected shortfall estimator for $$\alpha $$ α -mixing financial losses. Based on the Bahadur type representation, we further establish the Berry–Esseen bound of the nonparametric expected shortfall estimator. It is shown that the optimal rate can achieve nearly $$O(n^{-1/8})$$ O ( n - 1 / 8 ) under some appropriate conditions. We also carry out some numerical simulations and a real data example to support our theoretical results based on finite samples.

Suggested Citation

  • Xuejun Wang & Yi Wu & Wei Wang, 2024. "Nonparametric estimation of expected shortfall for α-mixing financial losses," Computational Statistics, Springer, vol. 39(6), pages 3157-3179, September.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:6:d:10.1007_s00180-023-01434-5
    DOI: 10.1007/s00180-023-01434-5
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    References listed on IDEAS

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    3. Frey, Rudiger & McNeil, Alexander J., 2002. "VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1317-1334, July.
    4. Song Xi Chen, 2008. "Nonparametric Estimation of Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 6(1), pages 87-107, Winter.
    5. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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