Error Correction and MVGARCH-X

[spollard777]

I am estimating a bivariate GARCH-BEKK with the lagged error correction term. No problem.

I wish to now estimate a GARCH-BEKK with the lagged squared error correction term added to variance equation. I can do this via the xregressor option with no problem as well. However, my estimated model returns 3 terms. I realize that 2 are for the respective variances and 1 is for the covariance. However, when I examine the literature on doing this, everyone reports the estimates for this term as a 1x2 matrix since this term is being added solely to each equation's variance. There is no mention of getting the estimates as a lower triangular matrix.

All seem to be using a 1x2 matrix, D for the inclusion of the squared error correction term. Then D would be [d11 d12]. Then H11 would be the regular BEKK formulation with d11^2 added to it. H22 would be have term d12^2 and then H12 would include d11*d12. Are the 3 estimates that are returned these 3 terms or is there another term being estimated for the cross equation term? Can you please let me know what the 3 estimates are for an xregressor term in this instance.

Regards,

Stephen Pollard

[TomDoan]

In general, the XREG terms in a RATS GARCH model look like the constant term in the variance x the regressor. Since the constant term in the variance for BEKK is the outer product of a triangular matrix, that's the form that's used. For a 2x2 case, that will have three values.

You'll have to use a MAXIMIZE variation in order to do a different form for this. I just posted a revised set of MAXIMIZE-based BEKK code; it should be a fairly modest change to handle that.