BEKK Interpretations for Variance/Covariance Equations

[cmcknigh]

Hello,

I am trying to interpret my multivariate BEKK model results in the context of the variance and covariance equations for 4 price return series. For example, the variance equation for one series and the covariance equation between series 1 and 2 can be represented by the attachment I have included in this post. My question is: How are the ARCH/GARCH/Constant estimates in the BEKK output presented? Are they squared? Not squared? I may need to manipulate some of these estimated parameters to get the "economic" interpretation and correct statistical significance.

Thank you for the help!


Curtis

[TomDoan]

The variance constants gets increasingly complicated as you get to the higher row numbers as it's a lower triangular matrix times its transpose. So the sigma22 will be c(2,1)^2+c(2,2)^2, sigma33 is c(3,1)^2+c(3,2)^2+c(3,3)^2, ...

However, it's been my general impression that these expansions of BEKK are a waste of paper.

[cmcknigh]

Hello Tom,

Thanks for the feedback on the variance constants. For the ARCH and GARCH parameters, can the parameters themselves (ex. A(1,3)) be interpreted as spillovers? Or do I need to square them or perform an interaction with the other terms first?

Thanks,

Curtis

[TomDoan]

Hello Tom,

Thanks for the feedback on the variance constants. For the ARCH and GARCH parameters, can the parameters themselves (ex. A(1,3)) be interpreted as spillovers? Or do I need to square them or perform an interaction with the other terms first?

Thanks,

Curtis

That's debatable. See

https://estima.com/newslett/Apr2019RATS ... pdf#page=3

Particularly in a 4 variable model (as opposed to a 2 variable model) each of those coefficients is entering into so many different elements of the covariance matrix that it's effectively impossible to interpret any bidirectional effect in isolation.