| This paper investigates the asymptotic theory for a new vector ARMA-GARCH model. The conditions for the strict stationarity, ergodicity, and the higher-order 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 only under the second-order moment of the unconditional errors, and the finite fourth-order moment of the conditional errors. This is also a new result, even for the univariate ARCH model. Under additional moment conditions, the asymptotic normality of the QMLE is also obtained for the vector ARMA-GARCH model, as well as a consistent estimator of the asymptotic covariance. |