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Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations

Author

Listed:
  • Abdou Kâ Diongue

    (UGB - Université Gaston Berger de Saint-Louis Sénégal)

  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Rodney C. Wolff

    (School of Mathematical Sciences [Brisbane] - QUT - Queensland University of Technology [Brisbane])

Abstract

In this paper, we discuss the class of Bilinear GATRCH (BL-GARCH) models which are capable of capturing simultaneously two key properties of non-linear time series: volatility clustering and leverage effects. It has been observed often that the marginal distributions of such time series have heavy tails; thus we examine the BL-GARCH model in a general setting under some non-Normal distributions. We investigate some probabilistic properties of this model and we propose and implement a maximum likelihood estimation (MLE) methodology. To evaluate the small-sample performance of this method for the various models, a Monte Carlo study is conducted. Finally, within-sample estimation properties are studied using S&P 500 daily returns, when the features of interest manifest as volatility clustering and leverage effects.

Suggested Citation

  • Abdou Kâ Diongue & Dominique Guegan & Rodney C. Wolff, 2008. "Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00270719, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00270719
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00270719v1
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    Cited by:

    1. Motelle, Sephooko & Biekpe, Nicholas, 2015. "Financial integration and stability in the Southern African development community," Journal of Economics and Business, Elsevier, vol. 79(C), pages 100-117.
    2. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," PSE-Ecole d'économie de Paris (Postprint) halshs-00368336, HAL.
    3. Charalampos Basdekis & Apostolos Christopoulos & Alexandros Gkolfinopoulos & Ioannis Katsampoxakis, 2022. "VaR as a risk management framework for the spot and futures tanker markets," Operational Research, Springer, vol. 22(4), pages 4287-4352, September.
    4. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," Post-Print halshs-00368336, HAL.

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