Distribution: Normal Inverse Gaussian Transformation and Scaling

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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

1
nigtransform(mu = 0, sigma = 1,  skew = 0, shape = 3)

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

The conditional non-time varying skewness and shape parameters estimated from the GARCH process (zeta-rho).

Details

The NIG transformation is taken from Rmetrics internal function and scaled as shown 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 NIG distribution functions.

Author(s)

Diethelm Wuertz for the Rmetrics R-port of the NIG transformation function.
Alexios Ghalanos for rgarch implementation.

References

Blaesild, P., The two-dimensional hyperbolic distribution and related distributions, with an application to Johannsen's bean data, 1981, Biometrika 68, 251-263.
Eberlein, E. and Prauss, K., The Generalized Hyperbolic Model Financial Derivatives and Risk Measures, 1998, Mathematical Finance, Bachelier Congress 2000.

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