fBasics (version 280.73)

ghFit: GH Distribution Fit

Description

Estimates the distrinbutional parameters for a generalized hyperbolic distribution.

Usage

ghFit(x, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = 1, 
    scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE, 
    title = NULL, description = NULL, ...)

Arguments

x

a numeric vector.

alpha, beta, delta, mu, lambda

The parameters are alpha, beta, delta, mu, and and lambda: shape parameter alpha; skewness parameter beta, abs(beta) is in the

scale

a logical flag, by default TRUE. Should the time series be scaled by its standard deviation to achieve a more stable optimization?

doplot

a logical flag. Should a plot be displayed?

span

x-coordinates for the plot, by default 100 values automatically selected and ranging between the 0.001, and 0.999 quantiles. Alternatively, you can specify the range by an expression like span=seq(min, max, times =

trace

a logical flag. Should the parameter estimation process be traced?

title

a character string which allows for a project title.

description

a character string which allows for a brief description.

...

parameters to be parsed.

Value

• returns a list with the following components:
• estimate
  the point at which the maximum value of the log liklihood function is obtained.
• minimum
  the value of the estimated maximum, i.e. the value of the log liklihood function.
• code
  an integer indicating why the optimization process terminated. 1: relative gradient is close to zero, current iterate is probably solution; 2: successive iterates within tolerance, current iterate is probably solution; 3: last global step failed to locate a point lower than estimate. Either estimate is an approximate local minimum of the function or steptol is too small; 4: iteration limit exceeded; 5: maximum step size stepmax exceeded five consecutive times. Either the function is unbounded below, becomes asymptotic to a finite value from above in some direction or stepmax is too small.
• gradient
  the gradient at the estimated maximum.
• steps
  number of function calls.
• Remark: The parameter estimation for the stable distribution via the maximum Log-Likelihood approach may take a quite long time.

Details

The function nlm is used to minimize the "negative" maximum log-likelihood function. nlm carries out a minimization using a Newton-type algorithm.

Examples

## ghFit -
   # Simulate random variates HYP(1.5, 0.3, 0.5, -1.0):
   set.seed(1953)
   s = rgh(n = 1000, alpha = 1.5, beta = 0.3, delta = 0.5, mu = -1.0) 

## ghFit -  
   # Fit Parameters:
   # Note, this may take some time.
   # Starting vector (1, 0, 1, mean(s)):
   ghFit(s, alpha = 1, beta = 0, delta = 1, mu = mean(s), doplot = TRUE)