[R-SIG-Finance] rugarch NIG shape and skew parameters

[alexios]

Andy,

(skew,shape) are the location-scale invariant parameters (\rho,\zeta) in 
one of the parametrizations of the GH distribution (the '2nd 
parametrization' in Prause 1999). They jointly map onto
(\alpha,\beta,\delta,\mu) - the standard parameters of the GH 
distribution as shown in equations 70-82 of Section 2.3.5 of the vignette.

The (\bar \alpha,\bar \beta) you are referring to is a different 
location-scale invariant parametrization (the '4th').

One of the nice features of the (\rho,\zeta) parametrization is that
you can immediately translate it to the (\xi,\chi) parametrization (the 
'3rd') which asymptotically describes the skewness and kurtosis, 
respectively, of the hyperbolic distribution (lambda=1). See 
Barndorff-Nielsen et al 1985 for details.

However, for the particular limiting case of the GH Skew Student 
(discussed seperately in Section 2.3.6), the \bar \beta
parametrization (skew) together with nu (shape) is used.

If you want to investigate the maximum domain of skewness-kurtosis of 
the various distributions, have a look at the skdomain function, an 
example of which is available on the 'Distributions Functions' section 
of this rather old post: 
http://unstarched.net/2013/02/27/whats-new-in-rugarch-ver-1-01-5/

Regards,

Alexios

On 02/07/2015 20:29, Andy Tang wrote:
> Hi Alex,
>
> In your rugarch package, the garch+nig model has coefficients of 'skew' and 'shape'. These two parameters map to alpha_bar/beta_bar, not alpha/beta in the NIG parameter set, right?
>
> Thanks
> Andy
>
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