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I am a bit confused about the formulation of the EGARCH(1,1) model.
First, we have the error term: $\epsilon_t=\sigma_t*\zeta_t$, where $\zeta_t$ is white noise.

Now the EGARCH(1,1) should be:
$$ log(\sigma_t^2)=w+\alpha_1*log(\sigma_{(t-1)}^2)+g(\zeta_t) $$ but instead I always see $g(\epsilon_t)$.
does anyone know why?

Thank you

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  • $\begingroup$ If you use latex then it works better if you add the $$ signs ;) $\endgroup$ – Ric Jun 8 '15 at 6:52
  • $\begingroup$ Yeh thanks. any idea about my question? $\endgroup$ – user3384794 Jun 8 '15 at 8:58
  • $\begingroup$ Good point, I will answer $\endgroup$ – Ric Jun 8 '15 at 9:02
  • $\begingroup$ You need a $\log$ on the lhs of the equation. $\endgroup$ – Ric Jun 8 '15 at 9:03
  • $\begingroup$ Yes of course, I must have missed it out $\endgroup$ – user3384794 Jun 8 '15 at 9:25
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Just a quick fix. Looking at the wikipedia entry of EGARCH: $g(\zeta_t)$ (the unit-scale random variable) seems correct - as you say.

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  • $\begingroup$ Yes but then everybody writes $g(\epsilon_t)$, not sure why $\endgroup$ – user3384794 Jun 8 '15 at 9:26
  • $\begingroup$ Could you post a link to a reference? $\endgroup$ – Ric Jun 8 '15 at 9:29

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