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trawl (version 0.2.2)

acf_DExp: Autocorrelation function of the double exponential trawl function

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

Value

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

Details

The trawl function is parametrised by parameters \(0\le w\le 1\) and \(\lambda_1, \lambda_2 > 0\) as follows: $$g(x) = w e^{\lambda_1 x}+(1-w) e^{\lambda_2 x}, \mbox{ for } x \le 0.$$ Its autocorrelation function is given by: $$r(x) = (w e^{-\lambda_1 x}/\lambda_1+(1-w) e^{-\lambda_2 x}/\lambda_2)/c, \mbox{ for } x \ge 0,$$ where $$c = w/\lambda_1+(1-w)/\lambda_2.$$

Examples

Run this code
# NOT RUN {
acf_DExp(1,0.3,0.1,2)
# }

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