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.
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).
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.
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.