R: Fit the Skew Hyperbolic Student t-Distribution to Data

skewhypFit {SkewHyperbolic}

R Documentation

Fit the Skew Hyperbolic Student t-Distribution to Data

Description

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

Usage

skewhypFit(x, freq = NULL, breaks = NULL, startValues = "LA",
           paramStart = NULL, method = "Nelder-Mead", hessian = TRUE,
           plots = FALSE, printOut = TRUE, controlBFGS = list(maxit = 200),
           controlNM = list(maxit = 1000), maxitNLM = 1500, ...)
## S3 method for class 'skewhypFit'
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(), ...)
## S3 method for class 'skewhypFit'
print(x,digits = max(3, getOption("digits") - 3),...)

Arguments

`x`	Data vector for `skewhypFit`. Object of class `"skewhypFit"` for `print.skewhypFit`.
`freq`	Vector of weights with length equal to length of `x`.
`breaks`	Breaks for histogram, defaults to those generated by `hist(x, plot = FALSE, right = FALSE).`If `startValues = "LA"` then 30 breaks are used by default.
`startValues`	Code giving the method of determining starting values for finding the maximum likelihood estimates of the parameters.
`paramStart`	If `startValues = "US"` the user must specify a vector of starting parameter values in the form `c(mu,delta,beta,nu)`.
`method`	Different optimisation methods to consider, see Details.
`hessian`	Logical; if `hessian = TRUE` the value of the hessian is returned.
`plots`	Logical; if `plots = TRUE` the histogram, log-histogram, Q-Q and P-P plots are printed.
`printOut`	Logical; if `printOut = TRUE` results of the fitting are printed.
`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.
`which`	If a subset of 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 plot change, see `par(ask = .)`.
`digits`	Desired number of digits when the object is printed.
`...`	Passes arguments to `optim`, `nlm`, `hist`, `logHist`, `qqskewhyp` and `ppskewhyp`.

Details

startValues can be either "US"(User-supplied) or "LA" (Linear approximation) If startValues = "US" then a value for paramStart must be supplied. For the details concerning the use of startValues and paramStart see skewhypFitStart.

The three optimisation methods currently available are:

"BFGS": Uses the quasi-Newton method "BFGS" as documented in optim.
"Nelder-Mead": Uses an implementation of the Nelder and Mead method as documented in optim.
"nlm": Uses the nlm function in R.

For the details of how to pass control information using optim and nlm, see optim and nlm.

Value

skewhypFit returns a list with components:

`param`	A vector giving the maximum likelihood estimates of the parameters in the form `c(mu,delta,beta,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 `optim` or `nlm` for details.
`iter`	Number of iterations of optimisation routine.
`x`	The data used to fit the distribution.
`xName`	Character string with the actual `x` argument name.
`paramStart`	Starting values of the parameters returned by `skewhypFitStart`.
`svName`	Name of the method used to find starting values.
`startValues`	Acronym of method used to find starting values.
`breaks`	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` if `startValues = "US"`, or `density` if `startValues = "LA"`.

Author(s)

David Scott d.scott@auckland.ac.nz, Fiona Grimson

References

Aas, K. and Haff, I. H. (2006). The Generalised Hyperbolic Skew Student's t-distribution, Journal of Financial Econometrics, 4, 275–309.

Examples

## See how well skewhypFit works
param <- c(0, 1, 4, 10)
data <- rskewhyp(500, param = param)
fit <- skewhypFit(data)
## Use data set NOK/EUR as per Aas&Haff
data(lrnokeur)
nkfit <- skewhypFit(lrnokeur, method = "nlm")
## Use data set DJI
data(lrdji)
djfit <- skewhypFit(lrdji)

[Package SkewHyperbolic version 0.4-2 Index]