Unconditional variance with external regressor in volatility model I am analysing the unconditional variance of a time series, with the rugarch package in R. However with an external regressor which is a dummy variable 0 before a certain  date and 1 after this date.
Here is the code:
specgarch <- ugarchspec(variance.model=list(model="sGARCH", external.regressors= dummy),
                        mean.model=list(armaOrder=c(0,0)), distribution="norm")

garchfit <- ugarchfit(data=return, spec=specgarch)
uncvariance(garchfit)  

My question is: How can the unconditional variance of this model be calculated and how can the conditional variance be calculated (i.e., when dummy = 0 and when dummy = 1)? How does rugarch do it? 
Here is the output:
mu                  omega        alpha1         beta1        vxreg1 
-1.938049e-04  1.428670e-06  5.485199e-02  9.420126e-01  1.751348e-06

and unconditional variance:
0.0007350932

 A: The conditional variance that you are looking for will be the fitted values of the conditional variance from the estimated GARCH model: (sigma(garchfit))^2.
The unconditional variance will be
$$ \sigma^2=\frac{\omega}{1-(\alpha+\beta)} $$
in the period where the dummy variable equals zero, and it will be
$$ \sigma^2=\frac{\omega+\gamma}{1-(\alpha+\beta)} $$
where the dummy variable equals one.  
$\omega$ stand for the intercept in the GARCH model,
$\alpha$ stands for the GARCH coefficient associated with the lagged squared error,
$\beta$ stands for the coeffcient associated with the lagged conditional variance, and
$\gamma$ stands for the coefficient associated with the dummy.
I doubt that the unconditional variance for the whole period makes sense if there actually is a structural break (as accounted by the dummy variable). I don't know how the uncvariance is calculated in "rugarch" but it should approximately equal to the simple variance as if the observations were assumed to be i.i.d.
For more details, you may refer to Tsay "Analysis of Financial Time Series" (2005, 2nd ed., p.114) for a simple GARCH model without the exogenous dummy. (Presence of a dummy does not make it much more complicated.)
