Asymmetric BEKK model

[sanjeev]

Hi

I am trying to fit VAR(2)- BEKK model to my weekly data of four return series with lags of forex reserves as the exogenous variable.Although i do not get autocorrelation in the residuals but there is a signficant autocorrelation in the squared residuals.However, if i fit asymmetric BEKK model, there is no autocorrelation in residuals and squared residuals.So, is it right to fit asymmetric BEKK model to my data? Moreover,I have a confusion with the interpretation of the asymmetry coefficients in the BEKK model.I am getting many negative coefficients in the D matrix.Is that right?

Thanks
Sanjeev

[TomDoan]

As with the A and B matrices, the D matrix also doesn't have the sign identified. If the D's seem to have the "wrong" sign, just multiply them all by -1 and you'll have exactly the same model.

[sanjeev]

Many thanks for the reply!

I think that the diagonal elements of the D matrix should be positive,i.e. own negative shocks of a variable should have a higher impact on the conditional variance than the positive shocks.But as you said the signs of the D matrix are not identified, is it ok to get the negative diagonal coefficients of D matrix?

Thanks,
Sanjeev

[TomDoan]

As I said, you can multiple the entire D matrix by -1 if you would like. If all the diagonal elements are showing up negative, then you would certainly do that. If the diagonals are a mix of signs, then they are a mix of signs whether you sign-flip or not. It's eaaier to make sense of the results if they all are signed postive, but if there are relatively high correlations among at least two of the shocks, it's certainly possible to have a mix of signs on the diagonal.