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

## Arguments

y |
a univariate time series (numeric vector). |

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 `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. Ignored if `NULL` .
Otherwise, data transformed before model is estimated. |

biasadj |
Use adjusted back-transformed mean for Box-Cox
transformations. If `TRUE` , point forecasts and fitted values are mean
forecast. Otherwise, these points can be considered the median of the
forecast densities. |

x |
Deprecated. Included for backwards compatibility. |

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

## Value

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.

## Details

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`

.

## 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`

, `auto.arima`

,
`forecast.fracdiff`

.

## Examples