The RATS Software Forum

Dear Tom,
I am estimating a TBEKK model and as you know, the variance equation is a lower triangular matrix because the coefficients of the upper diagonal are restricted. To estimate the mean equation therefore, I also estimated a restricted VAR with a lower triangular matrix so that the mean equation of the TBEKK is consistent with the variance equation. I wanted to ask if this is the right approach. I thought that estimating a full (unrestricted) VAR for the mean equation when the variance equation is restricted will not be appropriate. Your views will be very much appreciated.
Thank you

I don't see any reason the two should be related.

Thanks for the reply. So just be very sure, the mean equation of the TBEKK model can be estimated using the standard VAR without any restriction just like the VAR in the full BEKK model, is this correct?

I'm not sure what you mean. The mean model parameters are estimated jointly with the GARCH variance model. There are no special results for a full VAR vs a near VAR like there is for a least squares estimation.

I will try to be as clear as I can. First of all, I am estimating volatility spillover effects but I am treating a certain variable as exogenous which is why I am using the TBEKK in the first place (although I have also applied the full BEKK for comparison purposes). The issue I am confronted with is; if certain variables are treated as exogenous to other variable in the variance model which is the case in the TBEKK model because the model is a lower triangular matrix, should the same variables be treated as exogenous in the mean model as well so that there will be consistency in the treatment of the variables in both the mean model and the variance model?. Because certain variables are not allowed to affect other variables in variance model of the TBEKK, if similar restrictions are not applied to the mean model, the question that may arise is; why is a variable treated as exogenous in the variance model but not treated the same way in the mean model. In order words, is it required to identify the mean model in the TBEKK to be a lower triangular matrix in line with the variance model. This is what I did but am not sure if that is right.
Thank you once again.

If you are assuming that the variable is "exogenous", then yes, you would need a triangular model for both the mean and the variance.

Thank you so much for all the explanations.