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

bonjourbc9 multeesl at yahoo.co.uk
Tue Sep 1 06:29:06 CEST 2009

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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?
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