The RATS Software Forum

Can anyone help me with the following covariance stationarity contion question? The BEKK model is covariance stationary when the eigen values of A ⨂ A
+ B ⨂ B are less than 1, how can i calculate the covariance
stationarity in the presence of asymmetry (the Matrix D) or in the presence of exogenous variables?

If you have exogenous variables, you can't really talk about "stationarity" since the variances will change with the values of those.

I don't believe there's a simple condition for the asymmetric effect. You get the relatively simple condition for the standard BEKK because the expected value of A'u(t-1)u(t-1)'A is linear in the (presumed) stationary covariance matrix. By contrast, the expected value of the asymmetry term is a very unpleasant non-linear function of it involving integrals with correlated multivariate Normals.