ghyptransform: Distribution: Generalized Hyperbolic Transformation and...

In rugarch: Univariate GARCH Models

Distribution: Generalized Hyperbolic Transformation and Scaling

Description

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.

Usage

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

Arguments

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

Details

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

Value

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.

Author(s)

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

References

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.

rugarch documentation built on Sept. 30, 2024, 9:30 a.m.