acf_supIG function

Autocorrelation function of the supIG trawl function

Autocorrelation function of the supIG trawl function

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

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

Returns

The autocorrelation function of the supIG trawl function evaluated at x

Details

The trawl function is parametrised by the two parameters c("delta\n\\delta\n", "geq0 \\geq 0") and γ≥0\gamma \geq 0 as follows:

g(x)=(1−2xγ−2)−1/2exp⁡(δγ(1−(1−2xγ−2)1/2)),\mboxforx≤0. 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 δ\delta and γ\gamma are not simultaneously equal to zero. Its autocorrelation function is given by:

r(x)=exp⁡(δγ(1−1+2x/γ2)),\mboxforx≥0. r(x) = \exp(\delta\gamma (1-\sqrt{1+2 x/\gamma^2})), \mbox{ for } x\ge 0.

Examples

acf_supIG(1,0.3,0.1)
trawl packageRead PDF manual
  • Maintainer: Almut E. D. Veraart
  • License: GPL-3
  • Last published: 2021-02-22

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