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Estimation of value-at-risk by $$L^{p}$$ L p quantile regression

Author

Listed:
  • Peng Sun

    (Sichuan University of Science and Engineering)

  • Fuming Lin

    (Sichuan University of Science and Engineering
    South Sichuan Center for Applied Mathematics)

  • Haiyang Xu

    (Sichuan University of Science and Engineering)

  • Kaizhi Yu

    (Southwestern University of Finance and Economics)

Abstract

Exploring more accurate estimates of financial value at risk (VaR) has always been an important issue in applied statistics. To this end either quantile or expectile regression methods are widely employed at present, but an accumulating body of research indicates that $$L^{p}$$ L p quantile regression outweighs both quantile and expectile regression in many aspects. In view of this, the paper extends $$L^{p}$$ L p quantile regression to a general classical nonlinear conditional autoregressive model and proposes a new model called the conditional $$L^{p}$$ L p quantile nonlinear autoregressive regression model (CAR- $$L^{p}$$ L p -quantile model for short). Limit theorems for regression estimators are proved in mild conditions, and algorithms are provided for obtaining parameter estimates and the optimal value of p. Simulation study of estimation’s quality is given. Then, a CLVaR method calculating VaR based on the CAR- $$L^{p}$$ L p -quantile model is elaborated. Finally, a real data analysis is conducted to illustrate virtues of our proposed methods.

Suggested Citation

  • Peng Sun & Fuming Lin & Haiyang Xu & Kaizhi Yu, 2025. "Estimation of value-at-risk by $$L^{p}$$ L p quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(1), pages 25-59, February.
  • Handle: RePEc:spr:aistmt:v:77:y:2025:i:1:d:10.1007_s10463-024-00911-y
    DOI: 10.1007/s10463-024-00911-y
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    References listed on IDEAS

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