The validity of significance tests for BEKK models?

[avalokita]

Dear Tom:

When estimating BEKK models, the RATS software produces the results of estimated coefficients in the level form of C(i,j), A(i,j), B(i,j), accompanied with corresponding significance tests. Yet, BEKK is a nonlinear model in which squared parameters matter in its variance equation. According to Kearney and Patton (2000), significant estimates of C(i,j), A(i,j), and B(i,j) do not warrant a same result for their squared form C(i,j)^2, A(i,j)^2, and B(i,j)^. Therefore, in order to conduct significance tests, Kearney and Patton (2000) suggest that the expected value and the standard errors of these nonlinear functions should be found, rather than the first two moments of the individual parameters that constitute them. In that case, the results for BEKK models estimated by the RATS software seem to be susceptible to academic critics. How and what can we do to avoid these critics? Would you please provide an reasonable exponentiation to assure reviewers the validity of significance tests?


Reference
Kearney, C. and Patton, A. J. (2000) Multivariate GARCH modeling of exchange rate volatility transmission in the European monetary system. Financial Review, 35, 29–48.

[TomDoan]

Most of http://www.estima.com/forum/viewtopic.php?f=11&t=1500 is about converting BEKK estimates to the corresponding VECH estimates.

The relationship between the BEKK parameters and the corresponding VECH parameters is basically the relationship between structural (BEKK) and reduced form (VECH). When you can estimate structural parameters, that's usually considered superior to reduced form. So I'm not sure that the criticism is particularly well-placed.