Correct specification for modelling a AR(p)-GJR GARCH(1, 1) - skewed t using fGARCH
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?