[R-SIG-Finance] cdf of skewed t distribution using fGARCH vs skewt package

Diethelm Wuertz wuertz at itp.phys.ethz.ch
Mon Aug 24 07:41:22 CEST 2009

Alex Chan wrote:
> I ran a AR(p)-GARCH (1,1) - skewed t using the fGARCH package. When I tried to use the sstd option in fgarch to return the cdf of the  standardized residuals z and compared it with the results obtained using the skewt package, I obtained different results even though both skewed t dist are based on Fernandez and steel. Since the standardized inovations are supposed to be iid with mean o and variance 1, i used   psstd(z, mean = 0, sd = 1, nu , xi ). Anyone can explain why this might be the case? 
> Alex 
sstd means standardized skew student-t, the first s is important.

in the student-t the number of degrees of freedom is related to the 
variance, so you cannot use the usual student t.
you need a reformulated distribution for which the variance is always 1 
and a proper nu which does not
change the variance. This does the sstd.

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