arfima.whittle.new<-function(series1)

{

            #

            #   Computes Whittle MLE for ARFIMA(0,d,0) models

            #

            aux <- nlminb(start = 0.25, whittle.loglik.new, lo = 0., up = 0.499, series=series1)$parameters

            return(aux)

}

arfima.whittle.new<-function(series1)

{

            #

            #   Computes Whittle MLE for ARFIMA(0,d,0) models

            #

            aux <- nlminb(start = 0.25, whittle.loglik.new, lo = 0., up = 0.499, series=series1)$parameters

            return(aux)

}

 whittle.loglik.new<-function(x, series)

{

            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))

}