In «New Introduction to Multiple Time Series», page 90, we have the following formulas for the ML estimators of a stable Gaussian VAR$(p)$ process:
where $\tilde \alpha = vec(\tilde A_1,...,\tilde A_p)$.
And here is exactly where my doubt resides. If for $\tilde \alpha$ estimator, I need $\tilde \mu$ estimator, but then for $\tilde \mu$ I'm going to need also $\tilde \alpha$. So, how is this dependence broken, or is this solved by an iterative algorithm that will reach a fixed point?
I've also posted this question in CV, but I didn't get any answer.
Any help would be appreciated.