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

[Alexios Ghalanos]

1. Section 3.1 of the vignette discusses robust standard error calculation. The non-robust version is calculated using the hessian function from the numDeriv package. A search of the package source R folder for terms "hessian" or "grad" will surely reveal where to look.
2. Method vcov can be used to extract the parameter covariance matrix (with option to extract the robust one as well).
3. Try using scaling (fit.control) or increasing the default tolerance of the solver.
4. There is no point supplying code for the dataset when no one else has access to that (so this is not really a reproducible example).
5. You did not report the log likelihood of the two estimated models, so I cannot gauge if rugarch may have stopped at a non global optimum, in which case (3) may be useful.

Alexios

On 27 Mar 2014, at 03:18 PM, philippe <philippe.kappeler at hotmail.com> wrote:

> 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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