<p>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:</p>

<p><a href="https://i.sstatic.net/86d0u.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/86d0u.png" alt="enter image description here"></a></p>

<p>where $\tilde \alpha = vec(\tilde A_1,...,\tilde A_p)$.</p>

<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?</p>

<p>I've also posted <a href="https://stats.stackexchange.com/questions/331104/mle-in-a-stable-gaussian-varp-process-are-the-lutkepohl-formulas-correct">this question in CV</a>, but I didn't get any answer.</p>

<p>Any help would be appreciated.</p>

CC BY-SA 3.0
2018-03-07T22:52:43.110Z
What is the difference between $\tilde{\mu}$ and $\tilde{\mu}^*$?
caverac
CC BY-SA 3.0
2018-03-07T23:15:15.953Z
@caverac their dimension, only.  Both are vectors, with the same vector $\mu$ repeated. $\tilde \mu^*$ is $TK\times 1$, the other is $Kp\times 1$.
An old man in the sea.
CC BY-SA 3.0
2018-03-08T01:09:35.677Z
I will look into this, need a bit more context. Will come back to you later this week
caverac
<econometrics><time-series>
Max Likelihood Estimators of a stable Gaussian VAR$(p)$ process. Are the Lutkepohl formulas correct?
An old man in the sea.
# Max Likelihood Estimators of a stable Gaussian VAR$(p)$ process. Are the Lutkepohl formulas correct?

(Asked by: username_0 on 2018-03-04)

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:

[![enter image description here](https://i.sstatic.net/86d0u.png)](https://i.sstatic.net/86d0u.png)

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](https://stats.stackexchange.com/questions/331104/mle-in-a-stable-gaussian-varp-process-are-the-lutkepohl-formulas-correct), but I didn't get any answer.

Any help would be appreciated.

**Tags:** econometrics, time-series

> **Comments:**
> **username_1**: What is the difference between $\tilde{\mu}$ and $\tilde{\mu}^*$?  
> **username_0**: @username_1 their dimension, only.  Both are vectors, with the same vector $\mu$ repeated. $\tilde \mu^*$ is $TK\times 1$, the other is $Kp\times 1$.  
> **username_1**: I will look into this, need a bit more context. Will come back to you later this week  

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## 0 answers

