Before revision: Although stochastic volatility and GARCH models have been successful to describe the volatility dynamics of univariate asset returns, their natural extension to the multivariate models with dynamic correlations has been difficult due to several major problems.
After revision: Although stochastic volatility and GARCH models have been successful to describe the volatility dynamics of univariate asset returns, extending them to the multivariate models with dynamic correlations has been difficult due to several major problems.