Composed and Factor Composed Multivariate GARCH Models

In this paper we present a new type of multivariate GARCH model which we call the composed MGARCH and factor composed MGARCH models. We show sufficient conditions for the covariance stationarity of these processes and proof of the invariance of the models under linear combinations, an important property for factor modeling. Furthermore, we introduce an α-stable version of these models and fit a four dimensional α-stable composed MGARCH process to the returns on four German stocks included in the DAX index. We show in an in-sample analysis as well as in an out-of-sample analysis that the model outperforms the classical exponentially weighted moving average (EMWA) model introduced by RiskMetrics.