#===LONG MEMORY  ARFIMA Models =====
# generate a fractionally-differenced ARIMA(1,d,1) model given initial values

library(ts)
library(fracdiff)

ts.sim <- fracdiff.sim(3000, ar=.2, ma=.4, d=.3)

win.graph()
ts.plot(ts.sim$series)

win.graph()
acf(ts.sim$series)

win.graph()
acf(ts.sim$series, type="partial")

# estimate the parameters in an ARIMA(1,d,1) model for the simulated series
fracdiff(ts.sim$series, nar = 1, nma = 1)