acf_supIG {ambit}

Autocorrelation function of the supIG trawl function

Description

This function computes the autocorrelation function associated with the supIG trawl function.

Usage

acf_supIG(x, delta, gamma)

Arguments

x

The argument (lag) at which the autocorrelation function associated with the supIG trawl function will be evaluated

delta

parameter in the supIG trawl

gamma

parameter in the supIG trawl

Details

The trawl function is parametrised by the two parameters \delta \geq 0 and \gamma \geq 0 as follows:

g(x) = (1-2x\gamma^{-2})^{-1/2}\exp(\delta \gamma(1-(1-2x\gamma^{-2})^{1/2})), \mbox{ for } x \le 0.

It is assumed that \delta and \gamma are not simultaneously equal to zero. Its autocorrelation function is given by:

r(x) = \exp(\delta\gamma (1-\sqrt{1+2 x/\gamma^2})), \mbox{ for } x \ge 0.

Value

The autocorrelation function of the supIG trawl function evaluated at x

Examples

acf_supIG(1,0.3,0.1)