Fit a fractionally differenced ARFIMA model
An ARFIMA(p,d,q) model is selected and estimated automatically using the Hyndman-Khandakar (2008) algorithm to select p and q and the Haslett and Raftery (1989) algorithm to estimate the parameters including d.
arfima(x, drange=c(0, 0.5), estim=c("mle","ls"), lambda=NULL, ...)
- a univariate time series (numeric vector).
- Allowable values of d to be considered. Default of
c(0,0.5)ensures a stationary model is returned.
estim=="ls", then the ARMA parameters are calculated using the Haslett-Raftery algorithm. If
estim=="mle", then the ARMA parameters are calculated using full MLE via the
- Box-Cox transformation parameter. Ignored if NULL. Otherwise, data transformed before model is estimated.
- Other arguments passed to
auto.arimawhen selecting p and q.
This function combines
automatically select and estimate an ARFIMA model. The fractional differencing parameter is chosen
first assuming an ARFIMA(2,d,0) model. Then the data are fractionally differenced using
the estimated d and an ARMA model is selected for the resulting time series using
auto.arima. Finally, the full ARFIMA(p,d,q) model is re-estimated using
estim=="mle", the ARMA coefficients are refined using
- A list object of S3 class
"fracdiff", which is described in the
fracdiffdocumentation. A few additional objects are added to the list including
x(the original time series), and the
J. Haslett and A. E. Raftery (1989) Space-time Modelling with Long-memory Dependence: Assessing Ireland's Wind Power Resource (with discussion); Applied Statistics 38, 1-50. Hyndman, R.J. and Khandakar, Y. (2008) "Automatic time series forecasting: The forecast package for R", Journal of Statistical Software, 26(3).
x <- fracdiff.sim( 100, ma=-.4, d=.3)$series fit <- arfima(x) tsdisplay(residuals(fit))