acf_LM: 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
Value
The autocorrelation function of the long memory trawl function
evaluated at x
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
$$r(x)=(1+x/\alpha)^{(1-H)}, \mbox{ for } x \ge 0.$$