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

In SkewHyperbolic: The Skew Hyperbolic Student t-Distribution

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 [e-mail], 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.

See Also

optim, nlm, par, hist, density, logHist, qqskewhyp, ppskewhyp, dskewhyp and skewhypFitStart.

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)

SkewHyperbolic documentation built on Nov. 26, 2023, 3 p.m.