How to modify GARCH model to incorporate new terms ? about arch HOT 1 CLOSED

The model you have is observationally equivalent to a standard GJR_GARCH.

$\sigma_t^2 = \omega + \beta \sigma_{t-1}^2 + \gamma_1 \epsilon_{t-1}^2 I_{ [ \epsilon_{t-1} < 0] } + \eta \epsilon_{t-1}^2I_{ [ \epsilon_{t-1} > 0] } .$

is the same as

$\sigma_t^2 = \omega + \beta \sigma_{t-1}^2 + \gamma_2 \epsilon_{t-1}^2 I_{ [ \epsilon_{t-1} < 0] } + \alpha \epsilon_{t-1}^2 .$

where $\eta=\alpha$ and $\gamma_2 + \alpha = \gamma_1$.

from arch.