R: Fitting generalized hyperbolic distributions to multivariate...

fit.ghypmv {ghyp}

R Documentation

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)

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.

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.

Value

An object of class mle.ghyp.

Note

The variance gamma distribution becomes singular when \mathbf{x} - \mathbf{\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.

Author(s)

Wolfgang Breymann, David Luethi

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

  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)

[Package ghyp version 1.6.4 Index]