#
# R VERSION
#
arfima.whittle<-function(series)
{
#
#   Computes Whittle MLE for ARFIMA(0,d,0) models
#
optim(par = 0.25, whittle.loglik,gr=NULL,method = "L-BFGS-B", lo = 0., up = 0.499, series = series)$par
}
#
# AUXILIARY FUNCTIONS
#
whittle.loglik<-function(x, series)
{
#
#   Whittle Loglikelihood
#
series <- series - mean(series)
a <- fft(series)
a <- Mod(a)^2
n <- length(series)
a <- a/(2 * pi * n)
m <- n/2
#
#Fourier frequencies
#
w <- (2 * pi * (1:m))/n
#
#Spectral Density:
#
b <- fn.density(w, x)
#
#  Calculate sigma^2
#
sigma2 <- (2 * sum(a[1:m]/b))/n
#
#  Whittle Log-likelihood
#
loglik <- 2 * pi * (sum(log(b)) + sum(a[1:m]/b)/sigma2)
return(loglik/n + pi * log(sigma2))
}
fn.density<-function(x, d)
{
#
#  Spectral density of an ARFIMA(0,d,0) process
#
	a <- (2 * sin(x/2))^(-2 * d)
	a <- a/(2 * pi)
	return(a)
}