Cermeno Grier Panel GARCH

Cermeño and Grier(2006) propose a number of models which apply individual homogeneity to various parameters in a multivariate GARCH model. It's important to note that (effectively) all multivariate GARCH models are applied to a "panel data set", in the sense that the data are a set of time series data for each of a number of individuals. However, in the typical multivariate GARCH model, the linkages between the equations are generally fairly minor. For instance, in a CC model, the mean and variance equations are separately parameterized across individuals and the only connection is through the contemporaneous correlation—in effect, you have a "seemingly unrelated regression" with GARCH error processes. However, if the dynamics for individuals are quite similar, there may be some gain to joint estimation with some parameters that are common to different equations. If the dynamics are not similar, you should not be using this.