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)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.
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.
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).
Diethelm Wuertz for the Rmetrics R-port of the nig transformation function.
Alexios Ghalanos for rugarch implementation.
The GHYP transformation is taken from Rmetrics internal function and scaled as in Blaesild (see 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.