[R-SIG-Finance] Different significance of parameter estimation in GARCH models using r (rugarch & fGarch package)

[philippe]

I have been working with the two packages fGarch and rugarch to fit a
GARCH(1,1) model to my exchange rate time series consisting of 3980 daily
log-returns.

Code:
fx_rates <- data.frame(read.csv("WMCOFixingsTimeSeries.csv", header=T,
sep=";", stringsAsFactors=FALSE))
EURUSD <- ts(diff(log(fx_rates$EURUSD), lag=1), frequency=1)

#GARCH(1,1)
library(timeSeries)
library(fGarch)
x <- EURUSD
fit <- garchFit(~garch(1,1), data=x, cond.dist="std", trace=F,
include.mean=F)
fit at fit$matcoef

library(rugarch)
spec <- ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1,
1)),
                   mean.model=list(armaOrder=c(0,0), include.mean=F),
distribution.model="std")
gfit <- ugarchfit(spec, x, solver="hybrid",
fit.control=list(stationarity=1))
gfit at fit$matcoef

The two models show the following results:

fGarch:

fit at fit$matcoef 
            Estimate         Std. Error          t value     Pr(>|t|) 
omega  1.372270e-07  6.206406e-08   2.211054  2.703207e-02 
alpha1  2.695012e-02  3.681467e-03   7.320484  2.471356e-13 
beta1   9.697648e-01  3.961845e-03 244.776060 0.000000e+00 
shape   8.969562e+00 1.264957e+00   7.090804  1.333378e-12
rugarch:

gfit at fit$matcoef
           Estimate              Std. Error         t value     Pr(>|t|)
omega  1.346631e-07  3.664294e-07    0.3675008   7.132455e-01
alpha1  2.638156e-02  2.364896e-03   11.1554837  0.000000e+00
beta1   9.703710e-01  1.999087e-03 485.4070764   0.000000e+00
shape   8.951322e+00 1.671404e+00    5.3555696   8.528729e-08

I have found a thread
http://r.789695.n4.nabble.com/Comparison-between-rugarch-and-fGarch-td4683770.html
on why the estimates are not identical, however I can't figure out the big
difference in the standard errors and therethrough the different
significancs for omega. Furthermore, I was not able to detect how the
standard errors are computed by investigating the source code of the rugarch
package. The difference is not caused by the stationarity constraint as
omega remains insignificant. Does anybody know how the standard errors of
the estimated parameters (omega, alpha, beta and nu (shape)) are calculated?
If possible I would like to proceed with the rugarch package, as I wish to
forecast volatility and determine VaR measures. rugarch has shown to a very
profound package for this intentions. Thank you for your support.



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