Multivariate GARCH with dynamic beta

We investigate a solution for the problems related to the application of multivariate GARCH models to markets with a large number of stocks by restricting the form of the conditional covariance matrix and by introducing a system of recursion formals. The model is based on a decomposition of the conditional covariance matrix into two components and requires only six parameters to be estimated. The first component can be interpreted as the market factor, all remaining components are assumed to be equal. This allow the analytical calculation of the inverse covariance matrix. The factors are dynamic and therefore enable to describe dynamic beta coefficients. We compare the estimated covariances for the S&P500 market with those of other GARCH models and find that they are competitive, despite the low number of parameters. As applications we use the daily values of beta coefficients to confirm a transition of the market in 2006. Furthermore we discuss the relationship of our model with the leverage effect.