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