If my one step ahead forecasts from GARCH(1,1)-X are: \begin{equation} \hat{h}_{t+1} = \hat{\alpha}_0 + \hat{\alpha}_1 \hat{u}^2_t + \hat{\beta}_1 \hat{h}_t + \hat{\psi} X_t \end{equation} Where $\hat{\alpha}_0,\, \hat{\alpha}_1,\,\hat{u}^2_t,\, \hat{\beta},\, \hat{h}_t$ and $ \hat{\psi}$ denote the GARCH(1,1)-X estimates of $\alpha_0, \alpha_1,u^2_t, \beta_1, h_t, \psi$ respectively.
Also, the one step ahead forecasts from a GJR-GARCH(1,1) forecasts are: \begin{equation} \hat{h}_{t+1} = \hat{\alpha}_0 + \hat{\alpha}_1 \hat{u}^2_t + \hat{\beta}_1 \hat{h}_t + \hat{\gamma} \hat{u}^2_{t}I_{u_{t}<0} +\hat{\psi} X_t \end{equation} Where $\hat{\alpha}_0,\, \hat{\alpha}_1,\,\hat{u}^2_t,\, \hat{\beta},\, \hat{h}_t,\, \hat{\gamma}$ and $ \hat{\psi}$ denote the GJR-GARCH(1,1)-X estimates of $\alpha_0, \alpha_1,u^2_t, \beta_1, h_t, \gamma$ and $ \psi$ respectively.
How can I write the h step ahead (h>1) for both equations the GARCH(1,1)-X and the GJR-GARCH(1,1)-X?