This paper presents theoretical results in the formulation and estimation of multivariate gen-
eralized ARCH models within simultaneous equations systems. A new parameterization of the
multivariate ARCH process is proposed and equivalence relations are discussed for the various
ARCH parameterizations. Constraints suffcient to guarantee the positive deffniteness of the con-
ditional covariance matrices are developed, and necessary and suffcient conditions for covariance
stationarity are presented. Identifcation and maximum likelihood estimation of the parameters in
the simultaneous equations context are also covered.