A closed-form estimator for the multivariate GARCH model

We provide a closed-form estimator based on the VARMA representation for the unrestricted multivariate GARCH(1,1) model. We show that the GARCH parameters can be derived analytically, using the autocovariances of the observed data, applying simple linear algebra tools. The resulting estimator is consistent and asymptotically normally distributed. sults provide also closed-form expressions for the parameters of the temporally aggregated multivariate GARCH(1,1) discussed in Hafner (2008) [15].