arfima: Fit a fractionally differenced ARFIMA model

In forecast: Forecasting Functions for Time Series and Linear Models

Fit a fractionally differenced ARFIMA model

Description

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.

Usage

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

Arguments

y	a numeric vector or univariate time series of class ts
drange	Allowable values of d to be considered. Default of c(0, 0.5) ensures a stationary model is returned.
estim	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 stats::arima() function.
model	Output from a previous call to arfima. If model is passed, this same model is fitted to y without re-estimating any parameters.
lambda	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.
biasadj	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.
xreg	Optionally, a numerical vector or matrix of external regressors, which must have the same number of rows as y. It should not be a data frame.
x	Deprecated. Included for backwards compatibility.
...	Other arguments passed to auto.arima() when selecting p and q.

Details

This function combines fracdiff::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::fracdiff(). If estim = "mle", the ARMA coefficients are refined using stats::arima().

Value

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

Author(s)

Rob J Hyndman and Farah Yasmeen

References

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).

See Also

fracdiff::fracdiff(), auto.arima(), forecast.fracdiff().

Examples

library(fracdiff)
x <- fracdiff.sim(100, ma = -0.4, d = 0.3)$series
fit <- arfima(x)
tsdisplay(residuals(fit))

forecast documentation built on March 18, 2026, 9:07 a.m.