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

Abdou Ka Diongue, Dominique Guegan () and Rodney C. Wolff ()
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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]

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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.

Keywords: elliptical distribution; leverage effects; Maximum Likelihood; Monte Carlo method; volatility clustering; BL-GARCH process; Monte Carlo simulations; estimation; distributions elliptiques; asymétrie; Processus bilinéaires; processus GARCH (search for similar items in EconPapers)
Date: 2008-03
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00270719v1
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Published in 2008

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Working Paper: Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations (2008)
Working Paper: Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations (2008)
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