Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/92700 
Year of Publication: 
2001
Series/Report no.: 
ISER Discussion Paper No. 549
Publisher: 
Osaka University, Institute of Social and Economic Research (ISER), Osaka
Abstract: 
This paper investigates the asymptotic theory for a vector ARMA-GARCH model. The conditions for the strict stationarity, ergodicity, and the higherorder moments of the model are established. Consistency of the quasi-maximum likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate ARCH and GARCH models. Moreover, the asymptotic normality of the QMLE for the vector ARCH model is obtained under only the second-order moment of the unconditional errors, and the finite fourth-order moment of the conditional errors. Under additional moment conditions, the asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA-GARCH models, as well as a consistent estimator of the asymptotic covariance.
Document Type: 
Working Paper

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