Asymptotic theory for multivariate GARCH processes |
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Authors: | F. Comte O. Lieberman |
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Affiliation: | a Laboratoire MAP5, FRE CNRS 2428, University of Paris 5, France b Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Haifa, Israel |
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Abstract: | We provide in this paper asymptotic theory for the multivariate GARCH(p,q) process. Strong consistency of the quasi-maximum likelihood estimator (MLE) is established by appealing to conditions given by Jeantheau (Econometric Theory14 (1998), 70) in conjunction with a result given by Boussama (Ergodicity, mixing and estimation in GARCH models, Ph.D. Dissertation, University of Paris 7, 1998) concerning the existence of a stationary and ergodic solution to the multivariate GARCH(p,q) process. We prove asymptotic normality of the quasi-MLE when the initial state is either stationary or fixed. |
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Keywords: | 62HI2 62FI2 |
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