In this chapter, we have already considered multiple univariate conditional volatility models. That is why in this recipe, we move to the multivariate setting. As a starting point, we consider Bollerslev's Constant Conditional Correlation GARCH (CCC-GARCH) model. The idea behind it is quite simple. The model consists of N univariate GARCH models, related to each other via a constant conditional correlation matrix R.
Like before, we start with the model's specification:
In the first equation, we represent the return series. The key difference between this representation and the one presented in previous recipes is the fact that, this time, we are considering multivariate returns, so rt is actually a vector of returns 
. The mean and error terms are represented analogically. To highlight this...
