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I'm studying economics and learning statistical topics only related to my fields.
In my textbook I read this formula for likelihood function, and I can't follow the rule.
$Y_t | Y_{t-1},Y_{t-2},\dots,Y_{-p+1} \sim N(0,\sum)$
$f(Y_t | Y_{t-1},Y_{t-2},\dots,Y_{-p+1},\theta)=(2\pi)^{-n/2} \sum^{-1/2}exp[(-1/2)(Y_t)'\sum^{-1}(Y_t)]$

I wonder why $(2\pi)^{-n/2}$ not $(2\pi)^{-1/2}$?
Isn't it from the normal density function formula $(2\pi)^{-1/2} \sum^{-1/2} exp[(-1/2)(Y_t)'\sum^{-1}(Y_t)]$?
I think it's a very simple and basic question to you guys but I can't find any hint from my textbook and internet.
Hope to find answer here. Thank you.

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    $\begingroup$ The use of "$\Sigma$" instead of "$\sigma$" for the variance in the first line suggests $Y_t$ is a vector, not a scalar. The appearance of "$n$" in the second line supports that interpretation and indicates the vector has length $n.$ Please, then, consult your textbook for the meaning of the notation. $\endgroup$
    – whuber ♦
    Commented Apr 2, 2023 at 13:55
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    $\begingroup$ @whuber Now I understand it. Thank you! $\endgroup$
    – guest
    Commented Apr 2, 2023 at 14:11

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