VarianceGamma (version 0.1-2)

vgFit: Fit the Variance Gamma to Data

Description

Fits a variance gamma distribution to data. Displays the histogram, log-histogram (both with fitted densities), Q-Q plot and P-P plot for the fit which has the maximum likelihood.

Usage

vgFit(x, freq = NULL, breaks = NULL, paramStart = NULL,
        startMethod = "Nelder-Mead", startValues = "SL",
        method = "Nelder-Mead", hessian = FALSE,
        plots = FALSE, printOut = FALSE,
        controlBFGS = list(maxit = 200),
        controlNM = list(maxit = 1000), maxitNLM = 1500, ...)

  ## S3 method for class 'vgFit':
print(x, digits = max(3, getOption("digits") - 3), ...)
  ## S3 method for class 'vgFit':
plot(x, which = 1:4,
       plotTitles = paste(c("Histogram of ","Log-Histogram of ",
                            "Q-Q Plot of ","P-P Plot of "), x$obsName,
                          sep = ""),
       ask = prod(par("mfcol")) < length(which) && dev.interactive(),
          ...)

Arguments

x

Data vector for vgFit. Object of class "vgFit" for print.vgFit and plot.vgFit.

freq

A vector of weights with length equal to length(x).

breaks

Breaks for histogram, defaults to those generated by hist(x, right = FALSE, plot = FALSE).

paramStart

A user specified starting parameter vector param taking the form c(vgC,sigma,theta,nu).

startMethod

Method used by vgFitStart in calls to optim, default is "Nelder-Mead". See Details.

startValues

Code giving the method of determining starting values for finding the maximum likelihood estimate of param, default method is "SL". See Details.

method

Different optimisation methods to consider, default is "Nelder-Mead". See Details.

hessian

Logical. If TRUE the value of the hessian is returned.

plots

Logical. If FALSE suppresses printing of the histogram, log-histogram, Q-Q plot and P-P plot.

printOut

Logical. If FALSE suppresses printing of results of fitting.

controlBFGS

A list of control parameters for optim when using the "BFGS" optimisation.

controlNM

A list of control parameters for optim when using the "Nelder-Mead" optimisation.

maxitNLM

A positive integer specifying the maximum number of iterations when using the "nlm" optimisation.

digits

Desired number of digits when the object is printed.

which

If a subset of the plots is required, specify a subset of the numbers 1:4.

plotTitles

Titles to appear above the plots.

ask

Logical. If TRUE, the user is asked before each plot, see par(ask = .).

...

Passes arguments to par, hist, logHist, qqhyperb and pphyperb.

Value

• A list with components:
• param
  A vector giving the maximum likelihood estimate of param, as (c,sigma,theta,nu).
• maxLik
  The value of the maximised log-likelihood.
• hessian
  If hessian was set to TRUE, the value of the hessian. Not present otherwise.
• method
  Optimisation method used.
• conv
  Convergence code. See the relevant documentation (either optim or nlm) for details on convergence.
• iter
  Number of iterations of optimisation routine.
• obs
  The data used to fit the hyperbolic distribution.
• obsName
  A character string with the actual obs argument name.
• paramStart
  Starting value of param returned by call to vgFitStart.
• svName
  Descriptive name for the method finding start values.
• startValues
  Acronym for the method of finding start values.
• breaks
  The cell boundaries found by a call to hist.
• midpoints
  The cell midpoints found by a call to hist.
• empDens
  The estimated density found by a call to hist.

code

method = "nlm"

itemize

• "BFGS"

item

• "Nelder-Mead"
• "nlm"

Details

startMethod can be either "BFGS" or "Nelder-Mead".

startValues can be one of the following:

• "US"

{User-supplied.} "SL"{Based on a fitted skew-Laplace distribution.} "MoM"{Method of moments.}

References

Seneta, E. (2004). Fitting the variance-gamma model to financial data. J. Appl. Prob., 41A:177--187.

See Also

optim, nlm, par, hist, logHist, qqvg, ppvg, dskewlap and vgFitStart.

Examples

param <- c(0,0.5,0,0.5)
dataVector <- rvg(500, param = param)
## See how well vgFit works
vgFit(dataVector)
vgFit(dataVector, plots = TRUE)
fit <- vgFit(dataVector)
par(mfrow = c(1,2))
plot(fit, which = c(1,3))

## Use nlm instead of default
param <- c(0,0.5,0,0.5)
dataVector <- rvg(500, param = param)
vgFit(dataVector, method = "nlm", hessian = TRUE)


## Use BFGS instead of deault
param <- c(0,0.5,0,0.5)
dataVector <- rvg(500, param = param)
vgFit(dataVector, method = "BFGS", hessian = TRUE)