Explanatory variable in variance equation Multivariate GARCH

[divac]

Hi,

I have 7 assets diagonal BEKK model with a single explanatory variable in the variance equation.

The only specification that does not give me a message about the matrix being not PSD (either in constant or Explanatory variable) is when constant is diagonal and Explanatory variable is RANK ONE matrix.

However, I am not sure on the implications of the choice of RANK ONE matrix in comparison with the alternatives such as scalar, indefinite matrix etc. Could anyone discuss a bit about the options (scalar, rank 1, full matrix etc.) especially for the Explanatory variables.

It does not seem to be a lot of literature on MGARCH with common Explanatory variables in variance. And my matrix algebra is just not there anymore.

Thanks in advance.
divac