ghyp (version 1.3.0)

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 = 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, 
           trace = TRUE, ...)   
           
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)

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.

Value

• An object of class mle.ghyp.

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, R�diger 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)

See Also

fit.ghypuv, fit.hypuv, fit.NIGuv, fit.VGuv, fit.tuv for univariate fitting routines.

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)