[R-SIG-Finance] [R-sig-finance] Correct specification for modelling a AR(p)-GJR GARCH(1, 1) - skewed t using fGARCH

alexios alexios at 4dscape.com
Tue Sep 1 21:38:19 CEST 2009

The skewness and shape parameters are distributional parameters of the
skew-student distribution of Fernandez and Steel. In order to get from
those distributional parameters to the sample skewness you use in excel
you need to apply a transformation relating to the theoretical moments
of the distribution (hint: have a look at the Rockinger/Jondeau page
www.hec.unil.ch/matlabcodes/econometrics.html for this).

I believe the skew and shape parameters of the sstd distribution are
invariant under linear transformation so whether you are talking about
standardized or non-standardized residuals they are the same.

HTH
-Alexios Ghalanos

bonjourbc9 wrote:
>
> Dear All,
> while waiting for a reply I tried to tidy up my codes abit and this is what
> I used to model a AR(1)-GARCH(1,1) with skewed student t distribution for
> the residuals.
>
>> fit1<-garchFit(EMEA~arma(1,0)+ garch(1,1),data=rr.emea ,cond.dist="sstd"
> ,trace=FALSE)
>
> This is what the fGARCH code returned;
>
> Error Analysis:
>         Estimate  Std. Error  t value Pr(>|t|)
> mu       0.08031     0.01902    4.223 2.41e-05 ***
> ar1      0.09528     0.01835    5.194 2.06e-07 ***
> omega    0.03102     0.00890    3.486  0.00049 ***
> alpha1   0.10835     0.01399    7.745 9.55e-15 ***
> beta1    0.87862     0.01519   57.848  < 2e-16 ***
> skew     0.88764     0.02320   38.261  < 2e-16 ***
> shape    7.37774     0.90894    8.117 4.44e-16 ***
>
> My question is what is this skew parameter for ?Is it the skewness of the
> residuals? or is it the skewness of the standardized residuals??
>
> I tried to extract both the residuals and standardized residuals using the
> following code;
>
>> residuals(fit1 , standardize=FALSE)
>> residuals(fit1,standardize=TRUE)
>
> When I copy the residuals into excel and calculate its skewness , both
> return me negative skewness of -0.5573 ( skew of standardized res) and
> -0.85492 (skew of res). So what exactly is the skewness of 0.88764?? I
> assume that the shape refers to the shape of the standardized errors?