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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:

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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.

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  • $\begingroup$ What is the difference between $\tilde{\mu}$ and $\tilde{\mu}^*$? $\endgroup$ – caverac Mar 7 '18 at 22:52
  • $\begingroup$ @caverac their dimension, only. Both are vectors, with the same vector $\mu$ repeated. $\tilde \mu^*$ is $TK\times 1$, the other is $Kp\times 1$. $\endgroup$ – An old man in the sea. Mar 7 '18 at 23:15
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    $\begingroup$ I will look into this, need a bit more context. Will come back to you later this week $\endgroup$ – caverac Mar 8 '18 at 1:09

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