acf_LM: Autocorrelation function of the long memory trawl function

In ambit: Simulation and Estimation of Ambit Processes

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 α > 0 as follows:

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

Its autocorrelation function is given by

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

Value

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

Examples

acf_LM(1,0.3,1.5)

ambit documentation built on Aug. 19, 2022, 5:19 p.m.