[R-SIG-Finance] rgarch and GH

[alexios]

The skew and shape parameters are the (\rho, \zeta) parametrization 
standardized for use in the (0, 1) GARCH process. The 'dlambda' 
represents the second shape parameter from the GIG mixing distribution 
(where dlambda = -0.5 is the Normal Inverse Gaussian distribution, 
dlambda=1 the Hypebolic, etc). For details see for example Prauss (1999)

The function:

ghyptransform(mu = 0, sigma = 1,  skew = 0, shape = 3, lambda = -0.5)

will transform (and scale by sigma) the returned parameters to the 
standard (\alpha,\beta,\delta,\mu) parametrization (ignore the returned 
parameter names...needs fixing. The returned values represent mu, delta, 
beta, alpha).

For VaR, you can use directly (without having to transform) the function:

qdist(distribution = "ghyp", p, mu = 0, sigma = 1, lambda = -0.5, skew = 
1, shape = 5).

where 'mu' would be the conditional mean (use the 'fitted' method to 
extract from fit object), and sigma the conditional sd (extracted using 
the 'sigma' method).

Hope that helps.

Regards,

Alexios Ghalanos


On 24/03/2011 02:03, ShyhWeir Tzang wrote:
> Dear Sir:
> Sorry for bothering you all. I am working on garch estimation using
> rgarch package assuming a generalized hyperbolic distribution. As I
> know, the number of estimated parameters of GH should have five
> paramters. However, I checked the output and found only three paramters:
> dlambda, skew and shape. Is it because the standardization of the GH by
> letting the mean and variance to be 0 and 1? To meet these two
> requirements, those paramters should at least have some values
> there. How can I extract the estimated values for all five parameters?
> What does dlambda represent? I want to extract those values as I need to
> calculate the VaR values by the model, which is still unclear to me how
> to use rgarch to calculate VaR. Enclosed is the code for testing.
> Appreciate for any help from you.
> Best regards,
> Shyh-Weir Tzang
> #
> library(rgarch)
> data(dji30ret)
> spec = ugarchspec(mean.model = list(armaOrder = c(0,0), include.mean =
> TRUE), variance.model = list(model = "sGARCH"), distribution.model = "ghyp")
> fit.dji=ugarchfit(spec,data=dji30ret[,"AA"], out.sample=1000)
>  > coef(fit.dji)
>             mu         omega        alpha1         beta1
> dlambda          skew         shape
>   5.218311e-04  2.906185e-06  3.720127e-02  9.555983e-01 -3.553546e+00
> 6.324228e-01  2.500494e-01
> #####
>
>
>
>