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I am modelling a GARCH(1,1) and a GARCH(1,1) with an asymmetric term.

$$h(t)=\omega+\alpha\varepsilon(t-1)^2+\beta\sigma(t-1)^2$$

and

$$h(t)=\omega+\alpha u(t-1)^2+\beta\sigma(t-1)^2 + \gamma (u(t-1)^2D)$$

$D$ takes a value of 1 if u is positive.

Will my log likelihood function change between these two models?

If so, how will it change?

Thanks!

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  • $\begingroup$ The Gaussian quasi log-likelihood function for the the GJR-GARCH(1,1) will be similar, but somewhat different because the variance parameter $h(t)$ is different, provided you have some assumptions on the terms $u$ and $\gamma$. $\endgroup$ – FunnyBuzer Jan 24 at 11:06
  • $\begingroup$ Great, how different, could you provide an example of a text where it will show me the difference. $\endgroup$ – user22485 Jan 25 at 7:54
  • $\begingroup$ Try having a look at these books: book1 or book2 $\endgroup$ – FunnyBuzer Jan 25 at 12:24
  • $\begingroup$ are you an expert with these books, could you direct me to specific pages? $\endgroup$ – user22485 Jan 25 at 14:11
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    $\begingroup$ I used them a long time ago. There are sections on the GJR-GARCH model, and you should have the log-likelihood derivation there $\endgroup$ – FunnyBuzer Jan 25 at 14:30

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