Calculation of VaR of a time series using a GARCH(1,1) ARMA(1,1) model Please, I've been stuck all the weekend in this problem, does someone know how find the Value at Risk $10$ days ahead (for example) using a GARCH($1,1$) ARMA($1,1$) Model.
Remark: 
If it is easier to write the answer in some programing language (like R), go ahead. Thank you very much again
 A: I assume you have a logarithmic return series of an asset of interest. 


*

*Fit an ARMA+GARCH model to your return series. You can do this by ugarchfit function in rugarch package in R  (you will have to choose what density you want to assume for the standardized residuals).

*Forecast conditional mean and conditional variance of the assumed parametric density 10 days ahead. You can do this by ugarchroll function in rugarch package in R.

*Given the forecasted mean and variance of the assumed density, you can obtain the 0.05 quantile of the distribution which will be your 5% VaR (you can use other quantiles, of course). You can do this by function qnorm for the normal density, qt for student density, or generally qsomethingelse for some other density in R.


There is a nice vignette for the rugarch package where you can learn more about ARMA+GARCH modelling (although not about VaR calculations). Also, this picture from Wikipedia helped me write this answer (I hope I got it correctly).
