fit.ghypuv: Fitting generalized hyperbolic distributions to univariate...

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

This function performs a maximum likelihood parameter estimation for univariate generalized hyperbolic distributions.

Usage

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fit.ghypuv(data, lambda = 1, alpha.bar = 0.5, mu = median(data),
           sigma = mad(data), gamma = 0,
           opt.pars = c(lambda = T, alpha.bar = T, mu = T,
                        sigma = T, gamma = !symmetric),
           symmetric = F, standardize = F, save.data = T,
           na.rm = T, silent = FALSE, ...)

fit.hypuv(data,
          opt.pars = c(alpha.bar = T, mu = T, sigma = T, gamma = !symmetric),
          symmetric = F, ...)

fit.NIGuv(data,
          opt.pars = c(alpha.bar = T, mu = T, sigma = T, gamma = !symmetric),
          symmetric = F, ...)

fit.VGuv(data, lambda = 1,
         opt.pars = c(lambda = T, mu = T, sigma = T, gamma = !symmetric),
         symmetric = F, ...)

fit.tuv(data, nu = 3.5,
        opt.pars = c(nu = T, mu = T, sigma = T, gamma = !symmetric),
        symmetric = F, ...)

fit.gaussuv(data, na.rm = T, save.data = T)

Arguments

data

An object coercible to a vector.

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 parameter sigma.

gamma

Starting value for the skewness parameter 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.

...

Arguments passed to optim and to fit.ghypuv when fitting special cases of the generalized hyperbolic distribution.

Details

The general-purpose optimization routine optim is used to maximize the loglikelihood function. 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 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.

Author(s)

Wolfgang Breymann, David Luethi

References

ghyp-package vignette in the doc folder or on http://cran.r-project.org/web/packages/ghyp/.

See Also

fit.ghypmv, fit.hypmv, fit.NIGmv, fit.VGmv, fit.tmv for multivariate fitting routines. ghyp.fit.info for information regarding the fitting procedure.

Examples

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  data(smi.stocks)

  nig.fit <- fit.NIGuv(smi.stocks[,"SMI"], opt.pars = c(alpha.bar = FALSE),
                       alpha.bar = 1, control = list(abstol = 1e-8))
  nig.fit

  summary(nig.fit)

  hist(nig.fit)

Example output

Loading required package: numDeriv
Loading required package: gplots

Attaching package: 'gplots'

The following object is masked from 'package:stats':

    lowess

[1] "Llh:  5.43442381858987E+03; Pars:  5.626297E-04,  8.875123E-03,  0.000000E+00"
[1] "Llh: -9.63118912675987E+04; Pars:  4.730129E-01,  8.875123E-03,  0.000000E+00"
[1] "Llh:  5.44117035692981E+03; Pars:  5.626297E-04,  1.423498E-02,  0.000000E+00"
[1] "Llh: -1.33159421324728E+05; Pars:  5.626297E-04,  8.875123E-03,  4.724503E-01"
[1] "Llh:  5.40585124384195E+03; Pars:  2.562630E-03,  1.423498E-02,  0.000000E+00"
[1] "Llh:  5.44117035692981E+03; Pars:  5.626297E-04,  1.423498E-02,  0.000000E+00"
[1] "Llh:  5.42996237953101E+03; Pars:  1.562630E-03,  1.424923E-02,  0.000000E+00"
[1] "Llh:  5.43079814576067E+03; Pars:  1.562630E-03,  1.422076E-02,  0.000000E+00"
[1] "Llh:  5.41369364563650E+03; Pars:  1.562630E-03,  1.423498E-02,  1.000000E-03"
[1] "Llh:  5.43906676328363E+03; Pars:  1.562630E-03,  1.423498E-02, -1.000000E-03"
[1] "Llh:  5.44117035692981E+03; Pars:  5.626297E-04,  1.423498E-02,  0.000000E+00"
[1] "Llh:  5.42137059007665E+03; Pars: -1.437370E-03,  1.423498E-02,  0.000000E+00"
[1] "Llh:  5.43772029929769E+03; Pars: -4.373703E-04,  1.424923E-02,  0.000000E+00"
[1] "Llh:  5.43857178038201E+03; Pars: -4.373703E-04,  1.422076E-02,  0.000000E+00"
[1] "Llh:  5.43892892734741E+03; Pars: -4.373703E-04,  1.423498E-02,  1.000000E-03"
[1] "Llh:  5.42938207221730E+03; Pars: -4.373703E-04,  1.423498E-02, -1.000000E-03"
[1] "Llh:  5.42996237953101E+03; Pars:  1.562630E-03,  1.424923E-02,  0.000000E+00"
[1] "Llh:  5.43772029929769E+03; Pars: -4.373703E-04,  1.424923E-02,  0.000000E+00"
[1] "Llh:  5.44030385848315E+03; Pars:  5.626297E-04,  1.426348E-02,  0.000000E+00"
[1] "Llh:  5.44117035692981E+03; Pars:  5.626297E-04,  1.423498E-02,  0.000000E+00"
[1] "Llh:  5.43280955921200E+03; Pars:  5.626297E-04,  1.424923E-02,  1.000000E-03"
[1] "Llh:  5.44070688002371E+03; Pars:  5.626297E-04,  1.424923E-02, -1.000000E-03"
[1] "Llh:  5.43079814576067E+03; Pars:  1.562630E-03,  1.422076E-02,  0.000000E+00"
[1] "Llh:  5.43857178038201E+03; Pars: -4.373703E-04,  1.422076E-02,  0.000000E+00"
[1] "Llh:  5.44117035692981E+03; Pars:  5.626297E-04,  1.423498E-02,  0.000000E+00"
[1] "Llh:  5.44203031551468E+03; Pars:  5.626297E-04,  1.420654E-02,  0.000000E+00"
[1] "Llh:  5.43363797827799E+03; Pars:  5.626297E-04,  1.422076E-02,  1.000000E-03"
[1] "Llh:  5.44156695163584E+03; Pars:  5.626297E-04,  1.422076E-02, -1.000000E-03"
[1] "Llh:  5.41369364563650E+03; Pars:  1.562630E-03,  1.423498E-02,  1.000000E-03"
[1] "Llh:  5.43892892734741E+03; Pars: -4.373703E-04,  1.423498E-02,  1.000000E-03"
[1] "Llh:  5.43280955921200E+03; Pars:  5.626297E-04,  1.424923E-02,  1.000000E-03"
[1] "Llh:  5.43363797827799E+03; Pars:  5.626297E-04,  1.422076E-02,  1.000000E-03"
[1] "Llh:  5.41734544414001E+03; Pars:  5.626297E-04,  1.423498E-02,  2.000000E-03"
[1] "Llh:  5.44117035692981E+03; Pars:  5.626297E-04,  1.423498E-02,  0.000000E+00"
[1] "Llh:  5.43906676328363E+03; Pars:  1.562630E-03,  1.423498E-02, -1.000000E-03"
[1] "Llh:  5.42938207221730E+03; Pars: -4.373703E-04,  1.423498E-02, -1.000000E-03"
[1] "Llh:  5.44070688002371E+03; Pars:  5.626297E-04,  1.424923E-02, -1.000000E-03"
[1] "Llh:  5.44156695163584E+03; Pars:  5.626297E-04,  1.422076E-02, -1.000000E-03"
[1] "Llh:  5.44117035692981E+03; Pars:  5.626297E-04,  1.423498E-02,  0.000000E+00"
[1] "Llh:  5.43317170665703E+03; Pars:  5.626297E-04,  1.423498E-02, -2.000000E-03"
Symmetric Normal Inverse Gaussian Distribution:

Parameters:
   alpha.bar           mu        sigma        gamma 
1.0000000000 0.0005626297 0.0142349834 0.0000000000 

log-likelihood:
5441.17


Call:
fit.NIGuv(data = smi.stocks[, "SMI"], opt.pars = c(alpha.bar = FALSE),     alpha.bar = 1, control = list(abstol = 1e-08))

Symmetric Normal Inverse Gaussian Distribution:

Parameters:
   alpha.bar           mu        sigma        gamma 
1.0000000000 0.0005626297 0.0142349834 0.0000000000 

Call:
fit.NIGuv(data = smi.stocks[, "SMI"], opt.pars = c(alpha.bar = FALSE),     alpha.bar = 1, control = list(abstol = 1e-08))

Optimization information:
log-Likelihood:                5441.17 
AIC:                           -10876.34 
Fitted parameters:             mu, sigma, gamma;  (Number: 3)
Number of iterations:          4 
Converged:                     TRUE 

ghyp documentation built on May 2, 2019, 6:09 p.m.