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, standardize = F, nit = 2000, reltol = 1e-8, 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 = !symmetric), symmetric = F, ...) fit.NIGmv(data, opt.pars = c(alpha.bar = T, mu = T, sigma = T, gamma = !symmetric), symmetric = F, ...) fit.VGmv(data, lambda = 1, opt.pars = c(lambda = T, mu = T, sigma = T, gamma = !symmetric), symmetric = F, ...) fit.tmv(data, nu = 3.5, opt.pars = c(lambda = T, mu = T, sigma = T, gamma = !symmetric), symmetric = F, ...) fit.gaussmv(data, na.rm = T, save.data = T)
data |
An object coercible to a matrix . |
lambda |
Starting value for the shape parameter lambda . |
alpha.bar |
Starting value for the shape parameter alpha.bar . |
nu |
Starting value for the shape parameter nu (only used in case of a student-t distribution. It determines
the degree of freedom and is defined as -2*lambda .) |
mu |
Starting value for the location parameter mu . |
sigma |
Starting value for the dispersion matrix sigma . |
gamma |
Starting value for the skewness vecotr gamma . |
opt.pars |
A named logical vector which states which parameters should be fitted. |
symmetric |
If TRUE the skewness parameter gamma keeps zero. |
standardize |
If TRUE the sample will be standardized before fitting.
Afterwards, the parameters and log-likelihood et cetera will be back-transformed. |
save.data |
If TRUE data will be stored within the
mle.ghyp 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 Multi-Cycle 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.ghyp
.
The variance gamma distribution becomes singular when x - mu = 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.
Providing both arguments, opt.pars
and symmetric
respectively,
can result in a conflict when opt.pars['gamma']
and symmetric
are TRUE
. In this case symmetric
will dominate and
opt.pars['gamma']
is set to FALSE
.
Wolfgang Breymann, David Lüthi
Alexander J. McNeil, Rüdiger Frey, Paul Embrechts (2005) Quantitative
Risk Management, Concepts, Techniques and Tools
ghyp
-package vignette in the doc
folder or on http://cran.r-project.org/web/packages/ghyp/.
S-Plus and R 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), reltol = 0.01)