Multivariate variance targeting in the BEKK-GARCH model

Abstract

Summary In this paper, we consider asymptotic inference in the multivariate BEKK model based on (co)variance targeting (VT). By definition the VT estimator is a two-step estimator and the theory presented is based on expansions of the modified likelihood 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. The simulations included indicate that the multivariately induced higher-order moment constraints are necessary.