This paper considers asymptotic inference in the multivariate BEKK model
based on (co-)variance targeting (VT). By de…nition the VT estimator is a two-step
estimator and the theory presented is based on expansions of the modi…ed like-
lihood function, or estimating function, corresponding to these two steps. Strong
consistency is established under weak moment conditions, while sixth order moment
restrictions are imposed to establish asymptotic normality. Included simulations in-
dicate that the multivariately induced higher-order moment constraints are indeed
necessary.