portes (version 1.08)

fitstable: Fit Parameters to Stable Distributions, McCulloch (1986)

Description

The quantile method of McCullogh (1986).

Usage

fitstable(x)

Arguments

x

univariate or independent multivariate variables of dimension k.

Value

• matrix of k rows and 4 columns. k represents the number of the variables in the vector x and the columns with named components alpha, beta, scale, and location respectively.

Details

The quantile estimation method of McCulloch (1986) is used for each variable in x. It is highly reliable, fast and reasonably efficient especially bearing in mind that in most applications there is a lot of data.

References

Lin, J.-W. and McLeod A.I.(2008). "Portmanteau Tests for ARMA Models with Infinite Variance." Journal of Time Series Analysis, 29, 600-617. McCulloch, J. H. (1986). "Simple Consistent Estimator of Stable Distribution Parameters". Commun. Statist.--Simula., 15(4), 1109-1136.

See Also

There is also a function stableFit in the fBasics package for fitting stable distributions for univariate data but it does not work very well. This is the reason for fitstable. See also rstable, varima.sim,

Examples

## Univariate
x <- rstable(800, 1.7, 0, 1, 0)
fitstable(x)
## Multivariate
ALPHA <- c(1.3,1.6)
BETA <- c(0,0.2)
GAMMA <-c(1,1)
DELTA <-c(0,0.2)
x <- rstable(500, ALPHA, BETA, GAMMA, DELTA)
fitstable(x)