ghyptransform: Distribution: Generalized Hyperbolic Transformation and...

Description Usage Arguments Details Value Author(s) References


The function scales the distributions from the (0, 1) zeta-rho GARCH parametrization to the alpha-beta parametrization and performs the appropriate scaling to the parameters given the estimated sigma and mu.


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



Either the conditional time-varying (vector) or unconditional mean estimated from the GARCH process.


The conditional time-varying (vector) sigma estimated from the GARCH process.

skew, shape, lambda

The conditional non-time varying skewness (rho) and shape (zeta) parameters estimated from the GARCH process (zeta-rho), and the GHYP lambda parameter (‘dlambda’ in the estimation).


The GHYP transformation is taken from Rmetrics internal function and scaled as in Blaesild (see references).


A matrix of size nrows(sigma) x 4 of the scaled and transformed parameters to be used in the alpha-beta parametrized GHYP distribution functions.


Diethelm Wuertz for the Rmetrics R-port of the nig transformation function.
Alexios Ghalanos for rugarch implementation.


Blaesild, P. 1981, The two-dimensional hyperbolic distribution and related distributions, with an application to Johannsen's bean data, Biometrika, 68, 251–263.
Eberlein, E. and Prauss, K. 2000, The Generalized Hyperbolic Model Financial Derivatives and Risk Measures, Mathematical Finance Bachelier Congress, 245–267.

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