#===LONG MEMORY  ARFIMA Models =====
# generate a fractionally-differenced ARIMA(1,d,1) model given initial values
ts.sim <- arima.fracdiff.sim(model = list(d=.3, ar=.2, ma=.4), n = 3000)

tsplot(ts.sim)

acf(ts.sim)
acf(ts.sim, type="partial")

# estimate the parameters in an ARIMA(1,d,1) model for the simulated series
arima.fracdiff(ts.sim, model = list(ar = NA, ma = NA))