Hello,

I'm trying to simulate time series with various "colors" of noise to verify
some other code I've written.  I'm using the fractal package, specifically
FDSimulate.  I have a detailed question about this particular function, but
I'd also be happy to receive any suggestions for other packages, functions,
citations.

To the question: FDSimulate takes a delta parameter governing the
fractionally differenced process.  Using delta = 0 we get white noise, delta
= 0.5 pink, and delta = 1 red/"brown."  Everything seemed to be working
great for delta = 0 and 1, but at delta = 0.5 there were problems.  Using
the FDWhittle function (which should back-calculate delta from a series of
numbers) I investigated what's going on:

#########################
require(fractal)
these.delt <- rep(seq(0,1,length.out=100),rep(10,100))
est.delt <- numeric(1000)
# this takes a few seconds
for(i in 1:1000) {
    this.x <-
FDSimulate(rep(these.delt[i],1000),rep(1,1000),method="ce",seed=runif(1,1,10000))
    est.delt[i] <- FDWhittle(this.x)
}

plot(these.delt,est.delt,xlab="delta",ylab="estimated delta")
abline(0,1,col="red")
#########################

This plot shows that for FDSimulate(delta=0,...) we can back-calculate the
right value, but at FDSimulate(delta=0.5,...) there is a big jump from a
back-calculated delta of around 0.1 to one of 0.7 (when it should be 0.5).
At FDSimulate(delta=1,...) the given and back-calculated values line up.  So
my question is...which function is not doing its job (or which do I not
understand!), does FDSimulate not produce accurate time series, or does
FDWhittle not accurately estimate delta?  I tried using different methods in
FDSimulate but they threw the error:
Error in as.vector(.Call("RS_fractal_bootstrap_circulant_embedding", S,  :
  error in evaluating the argument 'x' in selecting a method for function
'as.vector'

If I am missing other useful functions for producing/estimating time series
of the fractional/long-memory type I would also welcome suggestions.

Thanks for your thoughts and insights!
Andy Rominger

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