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BL-GARCH model with elliptical distributed innovations

Author

Listed:
  • Abdou Kâ Diongue

    () (UFR SAT - Université Gaston Berger de Saint-Louis Sénégal)

  • Dominique Guegan

    () (PSE - Paris School of Economics, CES - Centre d'économie de la Sorbonne - UP1 - Université 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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00368340, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00368340
    DOI: 10.1080/00949650902773577
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00368340
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    Cited by:

    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. 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.

    More about this item

    Keywords

    volatility clustering; Maximum Likelihood; Monte Carlo method; BL-GARCH process; elliptical distribution; leverage effects;

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