How to combine BEKK and EGARCH

[huanpipt]

I want to estimate a bivariate EGARCH with BEKK estimation.
I wander if the bivariate EGARCH model can be estimated by BEKK,
because most bi- and multivariate EGARCH doesn't contain the covariance in the covariance matrix.
Futhermore, if EGARCH model can't be estimated by BEKK, Is there another way to extract the covariance.
I want to use the covariance and variance to calculate a hedge ratio, thus, I need to obtain the covariance first.

Thanks for your help.

[TomDoan]

All multivariate E-GARCH models that I've seen use the "E" model for individual equations, and so use CC or DCC. Although it's possible to compute exp and log functions for p.d. symmetric matrices (if H=PDP', exp(H)=Pexp(D)P' and log(H)=Plog(D)P', where exp(D) and log(D) are applied element by element to the eigenvalues), it's not clear that you would want to apply a BEKK transformation to that. After all, there's no reason the coefficients need to be positive in an EGARCH model, and, in fact, with the typical scale of series to which GARCH is applied, you would expect that the coefficient matrix on the intercept wouldn't have positive elements.