4.9.3 Properties of CCC-GARCH and Orthogonal GARCH
Both CCC-GARCH and orthogonal GARCH model time-varying standard deviations well. Where they fall short is in modeling time-varying correlations. CCC-GARCH assumes a constant conditional correlation matrix. Orthogonal GARCH offers a non-constant conditional correlation matrix, but the stochastic behavior of that correlation matrix is not modeled directly. It is an artifact of the model, and results are often unreasonable.