A closed-form estimator for the multivariate GARCH(1,1)(1,1) model

• We provide a closed-form estimator for the unrestricted multivariate GARCH(1,1).
• We show that all parameters can be estimated using basic linear algebra tools.
• We show that the estimator is consistent and asymptotically normal.
• We provide closed-form results for temporal aggregation of multivariate GARCH(1,1).

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.Our results provide also closed-form expressions for the parameters of the temporally aggregated multivariate GARCH(1,1) discussed in Hafner (2008) [15].