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.

我们通过限制条件协方差矩阵的形式并引入递归形式系统，来研究与将多元GARCH模型应用于具有大量股票的市场有关的问题的解决方案。该模型基于将条件协方差矩阵分解为两个分量，并且仅需要估计六个参数。第一个成分可以解释为市场因素，其余所有成分均假定为相等。这允许逆协方差矩阵的解析计算。这些因素是动态的，因此可以描述动态贝塔系数。我们比较了S＆P500市场的估计协方差与其他GARCH模型的协方差，发现尽管参数数量少，但它们具有竞争力。