fBasics (version 2110.79)

sghFit: Standardized GH Distribution Fit

Description

Estimates the distrinbutional parameters for a standardized generalized hyperbolic distribution.

Usage

sghFit(x, zeta = 1, rho = 0, lambda = 1, include.lambda = TRUE,
    scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE, 
    title = NULL, description = NULL, ...)

Arguments

x

a numeric vector.

zeta, rho, lambda

shape parameter zeta is positive, skewness parameter rho is in the range (-1, 1). and index parameter lambda, by default 1.

include.lambda

a logical flag, by default TRUE. Should the index parameter lambda included in the parameter estimate?

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.

Examples

## sghFit -
   # Simulate Random Variates:
   set.seed(1953)
   s = rsgh(n = 2000, zeta = 0.7, rho = 0.5, lambda = 0) 

## sghFit -  
   # Fit Parameters:
   sghFit(s, zeta = 1, rho = 0, lambda = 1, include.lambda = TRUE, 
     doplot = TRUE)