TY - JOUR
T1 - Asymptotic theory for multivariate GARCH processes
AU - Comte, F.
AU - Lieberman, O.
PY - 2003/1
Y1 - 2003/1
N2 - 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 Theory 14 (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.
AB - 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 Theory 14 (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.
KW - Asymptotic normality
KW - BEKK
KW - Consistency
KW - GARCH
KW - Martingale CLT
UR - http://www.scopus.com/inward/record.url?scp=0037289158&partnerID=8YFLogxK
U2 - 10.1016/S0047-259X(02)00009-X
DO - 10.1016/S0047-259X(02)00009-X
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AN - SCOPUS:0037289158
SN - 0047-259X
VL - 84
SP - 61
EP - 84
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 1
ER -