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BL-GARCH model with elliptical distributed innovations

Author

Listed:
  • Abdou Kâ Diongue

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

  • Dominique Guegan

    (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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • 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, 2010. "BL-GARCH model with elliptical distributed innovations," Post-Print halshs-00368340, HAL.
    • Handle: RePEc:hal:journl:halshs-00368340
    DOI: 10.1080/00949650902773577
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00368340
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    References listed on IDEAS

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    1. Marius-Cristian Frunza & Dominique Guegan, 2010. "Risk assessment for a Structured Product Specific to the CO2 Emission Permits Market," Documents de travail du Centre d'Economie de la Sorbonne 10054, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Marius-Cristian Frunza & Dominique Guegan & Antonin Lassoudière, 2010. "Dynamic factor analysis of carbon allowances prices: From classic Arbitrage Pricing Theory to Switching Regimes," Documents de travail du Centre d'Economie de la Sorbonne 10062, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Marius-Cristian Frunza & Dominique Guegan & Antonin Lassoudière, 2010. "Statistical evidence of tax fraud on the carbon allowances market," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00523458, HAL.
    4. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    5. Choi, M.S. & Park, J.A. & Hwang, S.Y., 2012. "Asymmetric GARCH processes featuring both threshold effect and bilinear structure," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 419-426.
    6. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," Post-Print halshs-00368336, HAL.
    7. Marius-Cristian Frunza & Dominique Guegan, 2010. "Risk Assessment for a Structured Product Specific to the CO2 Emission Permits Market," Post-Print halshs-00504209, HAL.

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