I am forecasting an equity return density using the uGarchRoll commandin R studio, specifying the standardized t-distribution as error distribution. The uGarchRoll command already forecasts the Value at Risk. However I find that the values forecasted are not the same as those calculated by myself. Generally, the Value at Risk forecast should be the same number as if I would be using the qt(p, df) command? Or at least the destandardized value?
An example: uGarchRoll forecasts: mu=0.1262, sigma = 1.059, df=4.68, VaR (5%) = -1.51
By testing via the command qt(0.05,4.68) I receive -2.045887
Destandardized value would be: mu + sigma * qt = -2.045887
What am I getting wrong? The uGarchRoll command is pretty standard so the mistake cannot really lie in there can it?