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Unified Bayesian conditional autoregressive risk measures using the skew exponential power distribution

Author

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  • Marco Bottone

    (Banca d’Italia)

  • Lea Petrella

    (Sapienza University of Rome)

  • Mauro Bernardi

    (University of Padua)

Abstract

Conditional Autoregressive Value-at-Risk and Conditional Autoregressive Expectile have become two popular approaches for direct measurement of market risk. Since their introduction several improvements both in the Bayesian and in the classical framework have been proposed to better account for asymmetry and local non-linearity. Here we propose a unified Bayesian Conditional Autoregressive Risk Measures approach by using the Skew Exponential Power distribution. Further, we extend the proposed models using a semiparametric P-Spline approximation answering for a flexible way to consider the presence of non-linearity. To make the statistical inference we adapt the MCMC algorithm proposed in Bernardi et al. (2018) to our case. The effectiveness of the whole approach is demonstrated using real data on daily return of five stock market indices.

Suggested Citation

  • Marco Bottone & Lea Petrella & Mauro Bernardi, 2021. "Unified Bayesian conditional autoregressive risk measures using the skew exponential power distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 1079-1107, September.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:3:d:10.1007_s10260-020-00550-6
    DOI: 10.1007/s10260-020-00550-6
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    Cited by:

    1. Beatrice Foroni & Luca Merlo & Lea Petrella, 2023. "Expectile hidden Markov regression models for analyzing cryptocurrency returns," Papers 2301.09722, arXiv.org, revised Jan 2024.
    2. Fabrizio Leisen & Luca Rossini & Cristiano Villa, 2020. "Loss-based approach to two-piece location-scale distributions with applications to dependent data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 309-333, June.
    3. Beatrice Foroni & Luca Merlo & Lea Petrella, 2023. "Quantile and expectile copula-based hidden Markov regression models for the analysis of the cryptocurrency market," Papers 2307.06400, arXiv.org.

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