Fitting qGARCH, eGARCH and nGARCH (with rugarch)

Hi

I need to fit a ARMA(1, 1)-qGARCH(1 ,1), ARMA(1, 1)-nGARCH(1, 1) and a
ARMA(1, 1)-eGARCH(1, 1) to be able to compare them, and see what fits my
data the best.

I have searched and searched, but I can't where it says how to do it. I
have fitted a ARMA(1, 1)-sGARCH(1, 1) and a ARMA(1, 1)-gjrGARCH(1, 1) with
the help of rugarch. Perhaps you can fit a nGARCH via "submodel" in
rugarch, but I do not understand this theoretically?

Here is my rugarch sample code - I have fitted with both in-mean and
without in-mean:

x = runif(100, min = 1, max = 125)
ar = data.frame(matrix(rexp(500, rate=.1), ncol = 5))


# with "in mean":
fit <- ugarchspec(variance.model     = list(model = "gjrGARCH",
                                                        garchOrder = c(1,
1)),
                              mean.model         = list(armaOrder = c(1,1),
                                                        include.mean = TRUE,
archm = TRUE,
                                                        external.regressors
= ar),
                              distribution.model = "sstd")
fitmodel <- ugarchfit(data = x, spec = fit)

# without "in mean"

fit2 <- ugarchspec(variance.model     = list(model = "gjrGARCH",
                                                       garchOrder = c(1,
1)),
                             mean.model         = list(armaOrder = c(1,1),
                                                       external.regressors =
ar),
                             distribution.model = "sstd")

fitmodel2 <- ugarchfit(data = x, spec = fit2)

Regards

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