ghyp-package {ghyp}

A package on the generalized hyperbolic distribution and its special cases

Description

This package provides detailed functionality for working with the univariate and multivariate Generalized Hyperbolic distribution and its special cases (Hyperbolic (hyp), Normal Inverse Gaussian (NIG), Variance Gamma (VG), skewed Student-t and Gaussian distribution). Especially, it contains fitting procedures, an AIC-based model selection routine, and functions for the computation of density, quantile, probability, random variates, expected shortfall and some portfolio optimization and plotting routines as well as the likelihood ratio test. In addition, it contains the Generalized Inverse Gaussian distribution.

Details

Initialize:

ghyp	Initialize a generalized hyperbolic distribution.
hyp	Initialize a hyperbolic distribution.
NIG	Initialize a normal inverse gaussian distribution.
VG	Initialize a variance gamma distribution.
student.t	Initialize a Student-t distribution.
gauss	Initialize a Gaussian distribution.

Density, distribution function, quantile function and random generation:

dghyp	Density of a generalized hyperbolic distribution.
pghyp	Distribution function of a generalized hyperbolic distribution.
qghyp	Quantile of a univariate generalized hyperbolic distribution.
rghyp	Random generation of a generalized hyperbolic distribution.

Fit to data:

fit.ghypuv	Fit a generalized hyperbolic distribution to univariate data.
fit.hypuv	Fit a hyperbolic distribution to univariate data.
fit.NIGuv	Fit a normal inverse gaussian distribution to univariate data.
fit.VGuv	Fit a variance gamma distribution to univariate data.
fit.tuv	Fit a skewed Student-t distribution to univariate data.
fit.gaussuv	Fit a Gaussian distribution to univariate data.
fit.ghypmv	Fit a generalized hyperbolic distribution to multivariate data.
fit.hypmv	Fit a hyperbolic distribution to multivariate data.
fit.NIGmv	Fit a normal inverse gaussian distribution to multivariate data.
fit.VGmv	Fit a variance gamma distribution to multivariate data.
fit.tmv	Fit a skewed Student-t distribution to multivariate data.
fit.gaussmv	Fit a Gaussian distribution to multivariate data.
stepAIC.ghyp	Perform a model selection based on the AIC.

Risk, performance and portfolio optimization:

ESghyp	Expected shortfall of a univariate generalized hyperbolic distribution.
ghyp.omega	Performance measure Omega based on a univariate ghyp distribution.
portfolio.optimize	Calculate optimal portfolios with respect to alternative risk measures.

Utilities:

mean	Returns the expected value.
vcov	Returns the variance(-covariance).
ghyp.skewness	Skewness of a univariate ghyp distribution.
ghyp.kurtosis	Kurtosis of a univariate ghyp distribution.
logLik	Returns Log-Likelihood of fitted ghyp objects.
AIC	Returns the Akaike's Information Criterion of fitted ghyp objects.
lik.ratio.test	Performs a likelihood-ratio test on fitted ghyp distributions.
[	Extract certain dimensions of a multivariate ghyp distribution.
scale	Scale ghyp distribution objects to zero expectation and/or unit variance.
transform	Transform a multivariate generalized hyperbolic distribution.
ghyp.moment	Moments of the univariate ghyp distribution.
coef	Parameters of a generalized hyperbolic distribution.
ghyp.data	Data of a (fitted) generalized hyperbolic distribution.
ghyp.fit.info	Information about the fitting procedure, log-likelihood and AIC value.
ghyp.name	Returns the name of the ghyp distribution or a subclass of it.
ghyp.dim	Returns the dimension of a ghyp object.
summary	Summary of a fitted generalized hyperbolic distribution.

Plot functions:

qqghyp	Perform a quantile-quantile plot of a (fitted) univariate ghyp distribution.
hist	Plot a histogram of a (fitted) univariate generalized hyperbolic distribution.
pairs	Produce a matrix of scatterplots with quantile-quantile plots on the diagonal.
plot	Plot the density of a univariate ghyp distribution.
lines	Add the density of a univariate ghyp distribution to a graphics device.

Generalized inverse gaussian distribution:

dgig	Density of a generalized inverse gaussian distribution
pgig	Distribution function of a generalized inverse gaussian distribution
qgig	Quantile of a generalized inverse gaussian distribution
ESgig	Expected shortfall of a generalized inverse gaussian distribution
rgig	Random generation of a generalized inverse gaussian distribution

Package vignette:
A document about generalized hyperbolic distributions can be found in the doc folder of this package or on https://cran.r-project.org/package=ghyp.

Existing solutions

There are packages like GeneralizedHyperbolic, HyperbolicDist, SkewHyperbolic, VarianceGamma and fBasics which cover the univariate generalized hyperbolic distribution and/or some of its special cases. However, the univariate case is contained in this package as well because we aim to provide a uniform interface to deal with generalized hyperbolic distribution. Recently an R port of the S-Plus library QRMlib was released. The package QRMlib contains fitting procedures for the multivariate NIG, hyp and skewed Student-t distribution but not for the generalized hyperbolic case. The package fMultivar implements a fitting routine for multivariate skewed Student-t distributions as well.

Object orientation

We follow an object-oriented programming approach in this package and introduce distribution objects. There are mainly four reasons for that:

• Unlike most distributions the GH distribution has quite a few parameters which have to fulfill some consistency requirements. Consistency checks can be performed uniquely when an object is initialized.

• Once initialized the common functions belonging to a distribution can be called conveniently by passing the distribution object. A repeated input of the parameters is avoided.

• Distributions returned from fitting procedures can be directly passed to, e.g., the density function since fitted distribution objects add information to the distribution object and consequently inherit from the class of the distribution object.

• Generic method dispatching can be used to provide a uniform interface to, e.g., plot the probability density of a specific distribution like plot(distribution.object). Additionally, one can take advantage of generic programming since R provides virtual classes and some forms of polymorphism.

Acknowledgement

This package has been partially developed in the framework of the COST-P10 “Physics of Risk” project. Financial support by the Swiss State Secretariat for Education and Research (SBF) is gratefully acknowledged.

Author(s)

David Luethi, Wolfgang Breymann

Institute of Data Analyses and Process Design (https://www.zhaw.ch/en/engineering/institutes-centres/idp/groups/data-analysis-and-statistics/)

Maintainer: Marc Weibel <[e-mail]>

References

Quantitative Risk Management: Concepts, Techniques and Tools by Alexander J. McNeil, Ruediger Frey and Paul Embrechts
Princeton Press, 2005

Intermediate probability: A computational approach by Marc Paolella
Wiley, 2007

S-Plus and R Library for Quantitative Risk Management QRMlib by Alexander J. McNeil (2005) and Scott Ulman (R-port) (2007)