garch vs garchFit - minimum sample size
In comparing garch{tseries} with garchFit{fGarch}, it seems that
the latter is more general, as it allows simultaneous estimation of an
arma model with possibly nonnormal garch or aparch noise, while 'garch'
fits only a garch model to a series assumed to have mean zero. I
simulated 10,000 observations from the garch(1,1) model given as an
example in the 'garchSim' help page, and got very similar answers from
'garch' as from 'garchFit' which I restricted the latter to fit the
model of the former:
x10k <- garchSim(n=10000)
summary(fit10k <- garch(x10k))
Estimate Std. Error t value Pr(>|t|)
a0 1.149e-06 1.467e-07 7.832 4.88e-15 ***
a1 1.032e-01 9.433e-03 10.942 < 2e-16 ***
b1 7.852e-01 2.039e-02 38.499 < 2e-16 ***
# simulated a0=1e-6, a1=0.1, b1=0.8
fit10k. <- garchFit(~garch(1,1), data=x10k, include.mean=FALSE)
summary(fit10k.)
Estimate Std. Error t value Pr(>|t|)
omega 1.148e-06 1.437e-07 7.99 1.33e-15 ***
alpha1 1.032e-01 9.027e-03 11.44 < 2e-16 ***
beta1 7.853e-01 1.963e-02 39.99 < 2e-16 ***
With only 100 observations, 'garch' complained 'singular
information' and quite early with different answers from garchFit:
summary(fit100 <- garch(x10k[1:100]))
Estimate Std. Error t value Pr(>|t|)
a0 9.842e-06 NA NA NA
a1 5.000e-02 NA NA NA
b1 5.000e-02 NA NA NA
fit100. <- garchFit(~garch(1,1), data=x10k[1:100], include.mean=FALSE)
summary(fit100.)
Estimate Std. Error t value Pr(>|t|)
omega 2.056e-06 1.677e-06 1.226 0.22022
alpha1 1.387e-01 1.193e-01 1.163 0.24469
beta1 6.704e-01 2.045e-01 3.278 0.00105 **
However, with 500 observations, 'garch' thought it converged and
again gave answers very similar to garchFit:
summary(fit500 <- garch(x10k[1:500]))
Estimate Std. Error t value Pr(>|t|)
a0 1.466e-06 6.432e-07 2.279 0.02265 *
a1 1.340e-01 4.405e-02 3.042 0.00235 **
b1 7.215e-01 9.292e-02 7.765 8.22e-15 ***
fit500. <- garchFit(~garch(1,1), data=x10k[1:500], include.mean=FALSE)
summary(fit500.)
Estimate Std. Error t value Pr(>|t|)
omega 1.450e-06 6.162e-07 2.352 0.01867 *
alpha1 1.340e-01 4.425e-02 3.029 0.00245 **
beta1 7.236e-01 8.430e-02 8.583 < 2e-16 ***
My conclusion from this is to use 'garchFit'.
By the way, the more general syntax for 'garchFit' is illustrated
by the following:
library(FinTS)
data(sp500)
library(fGarch)
spFit30.11 <- garchFit(sp500~arma(3,0)+garch(1,1), data=sp500)
Spencer
tom soyer wrote:
Spencer, take any data series and run garch vs. garchFit with various
sample size, and you will see garch needs a lot more data points to
get a good fit. Anyway, it probably doesn't matter if one always use a
sample size of >2,000. I was just courious.
On 2/12/08, *Spencer Graves* <spencer.graves at pdf.com
<mailto:spencer.graves at pdf.com>> wrote:
Why do you say that 'garch' requires more observations than
'garchFit'?
Can you outline documentation or tests you've performed?
Spencer
tom soyer wrote:
> Hi,
>
> It seems that the minimum sample size required by garch is much
larger than
> garchFit, does anyone know why? I am guessing between 1,000 and
2,000 for
> garch and ~500 for garchFit. Does anyone know the exact minimum
sample size
> for each?
>
> Thanks!
>
>
-- Tom