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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.


  drange = c(0, 0.5),
  estim = c("mle", "ls"),
  model = NULL,
  lambda = NULL,
  biasadj = FALSE,
  x = y,



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.


If 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 arima function.


Output from a previous call to arfima. If model is passed, this same model is fitted to y without re-estimating any parameters.


Box-Cox transformation parameter. If lambda="auto", then a transformation is automatically selected using BoxCox.lambda. The transformation is ignored if NULL. Otherwise, data transformed before model is estimated.


Use adjusted back-transformed mean for Box-Cox transformations. If transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If biasadj is TRUE, an adjustment will be made to produce mean forecasts and fitted values.


Deprecated. Included for backwards compatibility.


Other arguments passed to auto.arima when selecting p and q.


A list object of S3 class "fracdiff", which is described in the fracdiff documentation. A few additional objects are added to the list including x (the original time series), and the residuals and fitted values.


This function combines fracdiff and auto.arima to 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 fracdiff. If estim=="mle", the ARMA coefficients are refined using arima.


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).


Rob J Hyndman and Farah Yasmeen


x <- fracdiff.sim( 100, ma=-.4, d=.3)$series
fit <- arfima(x)