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