Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations
AbstractIn 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.
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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number b08027.
Length: 29 pages
Date of creation: Apr 2008
Date of revision:
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BL-GARCH process; elliptical distribution; leverage effects; maximum likelihood; Monte Carlo method; volatility clustering.;
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-05-17 (All new papers)
- NEP-ECM-2008-05-17 (Econometrics)
- NEP-ETS-2008-05-17 (Econometric Time Series)
- NEP-ORE-2008-05-17 (Operations Research)
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