acf_LM {ambit}

Autocorrelation function of the long memory trawl function

Description

This function computes the autocorrelation function associated with the long memory trawl function.

Usage

acf_LM(x, alpha, H)

Arguments

x

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

alpha

parameter in the long memory trawl

H

parameter in the long memory trawl

Details

The trawl function is parametrised by the two parameters H> 1 and \alpha > 0 as follows:

g(x) = (1-x/\alpha)^{-H}, \mbox{ for } x \le 0.

Its autocorrelation function is given by

r(x)=(1+x/\alpha)^{(1-H)}, \mbox{ for } x \ge 0.

Value

The autocorrelation function of the long memory trawl function evaluated at x

Examples

acf_LM(1,0.3,1.5)