What is the condition for underlying stochastic volatility processes to give a consistent covariance matrix?
I read in Hull that in order to have a consistent covariance matrix, volatility parameters should be estimated using same model. Does that mean, for example, if I am using a Garch(1,1) model with some parameters, I should use the same parameters for all underlying? Or it is just enough to have Garch(1,1) and not necessarily the same parameters.
In either case, what would be a solution if the underlyings obviously fall under different models?