A closed-form estimator for the multivariate GARCH(1,1) model (Q391807)

Estimating a multivariate GARCH(1,1) model is a challenging task. The most common tool for this purpose is the quasi maximum likelihood (QML) estimator, which requires rather sophisticated optimization techniques and is plagued by numerical problems. This paper presents a simple and fast method of moments which makes the estimation of the model more accessible. The results represent the multivariate generalization of the analytical results of \textit{D. Kristensen} and \textit{O. Linton} [Econom. Theory 22, No. 2, 323--337 (2006; Zbl 1138.62050)]. It is shown that the GARCH parametrs can be derived analytically using the autocovariances of the observed data, applying simple linear algebra tools. The resulting estimator is consistent and aymptotically normally distributed.