fit.ghypmv {ghyp} | R Documentation |
Perform a maximum likelihood estimation of the parameters of a multivariate generalized hyperbolic distribution by using an Expectation Maximization (EM) based algorithm.
fit.ghypmv(data, lambda = 1, alpha.bar = 1, mu = NULL, sigma = NULL, gamma = NULL, opt.pars = c(lambda = T, alpha.bar = T, mu = T, sigma = T, gamma = !symmetric), symmetric = F, nit = 2000, reltol = 1e-10, abstol = reltol * 10, na.rm = F, silent = FALSE, save.data = T, ...) fit.hypmv(data, opt.pars = c(alpha.bar = T, mu = T, sigma = T, gamma = T), ...) fit.NIGmv(data, opt.pars = c(alpha.bar = T, mu = T, sigma = T, gamma = T), ...) fit.VGmv(data, lambda = 1, opt.pars = c(lambda = T, mu = T, sigma = T, gamma = T), ...) fit.tmv(data, nu = 4, opt.pars = c(lambda = T, mu = T, sigma = T, gamma = T), ...)
data |
A vector or univariate data.frame . |
lambda |
Shape parameter. |
alpha.bar |
Shape parameter. |
nu |
Shape parameter only used in case of a student-t distribution. It determines
the degree of freedom and is defined as -2*lambda . |
mu |
Location parameter. |
sigma |
Dispersion parameter. |
gamma |
Skewness parameter. |
opt.pars |
A named logical vector which states which parameters should be fitted. |
symmetric |
If TRUE the skewness parameter gamma keeps zero. |
save.data |
If TRUE data will be stored within the
mle.ghypmv object. |
na.rm |
If TRUE missing values will be removed from data . |
silent |
If TRUE no prompts will appear in the console. |
nit |
Maximal number of iterations of the expectation maximation algorithm. |
reltol |
Relative convergence tolerance. |
abstol |
Absolute convergence tolerance. |
... |
Arguments passed to optim and to fit.ghypmv when
fitting special cases of the generalized hyperbolic distribution. |
This function uses a modified EM algorithm which is called Multicycle Expectation
Conditional Maximization (MCECM)
algorithm. This algorithm is sketched in the vignette of this package which
can be found in the doc
folder. A more detailed description is provided
by the book Quantitative Risk Management, Concepts, Techniques and Tools
(see “References”).
The general-purpose optimization routine optim
is used to maximize
the loglikelihood function of the univariate mixing distribution.
The default method is that of Nelder and Mead which
uses only function values. Parameters of optim
can be passed via
the ... argument of the fitting routines.
An object of class mle.ghypmv
.
The variance gamma distribution becomes singular when x - m = 0
. This singularity
is catched and the reduced density function is computed. Because the transition is
not smooth in the numerical implementation this can rarely result in nonsensical
fits.
Wolfgang Breymann, David Lüthi
Alexander J. McNeil, Rüdiger Frey, Paul Embrechts (2005) Quantitative
Risk Management, Concepts, Techniques and Tools
S-Plus library QRMlib (see http://www.math.ethz.ch/~mcneil/book/QRMlib.html).
fit.ghypuv
, fit.hypuv
, fit.NIGuv
,
fit.VGuv
, fit.tuv
for univariate fitting routines.
data(smi.stocks) fit.ghypmv(data=smi.stocks,opt.pars=c(lambda=FALSE),lambda=2, control=list(rel.tol=1e-5, abs.tol=1e-5), abstol=0.01, reltol=0.01)