Hypothesis test on BEKK coefficients

[paldejong]

I am hoping you could recommend the appropriate procedure to test for the difference of BEKK coefficients between two models with similar data; for example the difference between B(2,1) of one model versus the B(2,1) of the next. My initial thought was to use a version of the Wald test but I am not sure if the outcome of that test would actually test the correct hypothesis.

Thank you,

Pieter de Jong

[TomDoan]

Comparing two separate estimators is a tricky business. If the data are independent (disjoint subsamples for instance), then the covariance matrix of the difference in the estimators is the sum of the separate covariance matrices. It sounds, however, like that's not the case. If the data are "similar" then the estimators are likely to be correlated, and there's no simple way to combine them.

[paldejong]

Thank you for your response. Let's assume that the data are independent, how would I define the covariance matrices for the individual beta coefficients. For the entire beta matrix (%beta), it would be %xx; would it be %xx(i,i) for %beta(i)?

Thank you,

Pieter

[TomDoan]

Yes. However, it's not clear that it's particularly interesting to test for equality between single coefficients out of a BEKK---the coefficients within a model are often highly correlated with each other, as if they weren't you probably wouldn't be doing a multivariate GARCH model. As a result, you will probably almost never reject equality between say B(1,1) in one model and B(1,1) in another.