Difference between VECH AND BEKK Model

[upani]

Dear All,

Would you please clarify me the basic difference between vech and bekk model for multivariate volatility. Can we apply both model or which model is superior?

With sincere regards,
Upananda

[TomDoan]

Dear All,

Would you please clarify me the basic difference between vech and bekk model for multivariate volatility. Can we apply both model or which model is superior?

With sincere regards,
Upananda

The VECH model is of more theoretical than practical interest---I'm not sure I remember the last time I saw a paper that estimated a VECH-GARCH. It's impractically complex with more than two variables. However, the VECH representation is very convenient for doing variance forecasts or variance IRF's, which is why we have the @MVGARCHTOVECH procedure, and version 9 has the VECHMAT option, to convert other models to VECH form for forecasting purposes.

BEKK is a tightly restricted form of the VECH model which creates a forcibly positive definite covariance matrix recursion. (The unrestricted VECH doesn't). The DVECH (or standard) multivariate GARCH model is also a special (even more) tightly restricted form of the VECH which, however, doesn't enforce positive definiteness. The main competitors in empirical work, particularly with 3 or 4 variables, are the BEKK and some form of CC or DCC model. Beyond 4 variables, you usually need to go to CC/DCC models.

[Darth Nisis]

Dear All,

Would you please clarify me the basic difference between vech and bekk model for multivariate volatility. Can we apply both model or which model is superior?

With sincere regards,
Upananda

The VECH model is of more theoretical than practical interest---I'm not sure I remember the last time I saw a paper that estimated a VECH-GARCH. It's impractically complex with more than two variables. However, the VECH representation is very convenient for doing variance forecasts or variance IRF's, which is why we have the @MVGARCHTOVECH procedure, and version 9 has the VECHMAT option, to convert other models to VECH form for forecasting purposes.

BEKK is a tightly restricted form of the VECH model which creates a forcibly positive definite covariance matrix recursion. (The unrestricted VECH doesn't). The DVECH (or standard) multivariate GARCH model is also a special (even more) tightly restricted form of the VECH which, however, doesn't enforce positive definiteness. The main competitors in empirical work, particularly with 3 or 4 variables, are the BEKK and some form of CC or DCC model. Beyond 4 variables, you usually need to go to CC/DCC models.

Dear Tom,

I now an unrestricted VECH model is not recommended, but nevertheless I'm trying to estimate a 4 variables VECH model in order to compare it with a BEKK model with the same variables. The purpose of the exercise is to compare the resulting Hafner & Herwartz VIRFs under the two models.

The estimate of the 4 variables VECH model converged, but when I analysed the output, i noted that most interaction coefficients were restricted either to 0, to 0.05 or to 0.45. Are this restrictions on purpose? I attached the output (by the way, I have RATS 9.00)

Best regards,

Juan

[TomDoan]

To be perfectly honest, I've never gotten a VECH model to converge with even 3 variables, much less 4, even if you start off the guess values from the BEKK or DVECH. There are just too many false "hills" that end up with near-singular matrices at some entry.