acf_DExp: Autocorrelation function of the double exponential trawl...

In trawl: Estimation and Simulation of Trawl Processes

Description

This function computes the autocorrelation function associated with the double exponential trawl function.

Usage

acf_DExp(x, w, lambda1, lambda2)

Arguments

x	The argument (lag) at which the autocorrelation function associated with the double exponential trawl function will be evaluated
w	parameter in the double exponential trawl
lambda1	parameter in the double exponential trawl
lambda2	parameter in the double exponential trawl

Details

The trawl function is parametrised by parameters 0≤ w≤ 1 and λ_1, λ_2 > 0 as follows:

g(x) = w e^{λ_1 x}+(1-w) e^{λ_2 x}, \mbox{ for } x ≤ 0.

Its autocorrelation function is given by:

r(x) = (w e^{-λ_1 x}/λ_1+(1-w) e^{-λ_2 x}/λ_2)/c, \mbox{ for } x ≥ 0,

where

c = w/λ_1+(1-w)/λ_2.

Value

The autocorrelation function of the double exponential trawl function evaluated at x

Examples

acf_DExp(1,0.3,0.1,2)

trawl documentation built on Feb. 23, 2021, 1:06 a.m.