fit.ghypmv: Fitting generalized hyperbolic distributions to multivariate data

Description

Perform a maximum likelihood estimation of the parameters of a multivariate generalized hyperbolic distribution by using an Expectation Maximization (EM) based algorithm.

Usage

fit.ghypmv(data, lambda = 1, alpha.bar = 1, mu = NULL, sigma = NULL,
           gamma = NULL, opt.pars = c(lambda = TRUE, alpha.bar = TRUE, mu = TRUE,
                                      sigma = TRUE, gamma = !symmetric),
           symmetric = FALSE, standardize = FALSE, nit = 2000, reltol = 1e-8,
           abstol = reltol * 10, na.rm = FALSE, silent = FALSE, save.data = TRUE,
           trace = TRUE, ...)
fit.hypmv(data,
          opt.pars = c(alpha.bar = TRUE, mu = TRUE, sigma = TRUE, gamma = !symmetric),
          symmetric = FALSE, ...)
fit.NIGmv(data,
          opt.pars = c(alpha.bar = TRUE, mu = TRUE, sigma = TRUE, gamma = !symmetric),
          symmetric = FALSE, ...)
fit.VGmv(data, lambda = 1,
         opt.pars = c(lambda = TRUE, mu = TRUE, sigma = TRUE, gamma = !symmetric),
         symmetric = FALSE, ...)
fit.tmv(data, nu = 3.5,
        opt.pars = c(lambda = TRUE, mu = TRUE, sigma = TRUE, gamma = !symmetric),
        symmetric = FALSE, ...)
fit.gaussmv(data, na.rm = TRUE, save.data = TRUE)

Value

An object of class mle.ghyp.

Arguments

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 (cf. ghyp.data).
trace: If TRUE the evolution of the parameter values during the fitting procedure will be traced and stored (cf. ghyp.fit.info).
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.

Author

Wolfgang Breymann, David Luethi

Details

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.

References

Alexander J. McNeil, Ruediger Frey, Paul Embrechts (2005) Quantitative Risk Management, Concepts, Techniques and Tools

ghyp-package vignette in the doc folder or on https://cran.r-project.org/package=ghyp.

S-Plus and R library QRMlib)

Examples

Run this code

  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)

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