# arfima

##### 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.

- Keywords
- ts

##### Usage

`arfima(x, drange=c(0, 0.5), estim=c("mle","ls"), lambda=NULL, ...)`

##### Arguments

- x
- 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`

- lambda
- Box-Cox transformation parameter. Ignored if NULL. Otherwise, data transformed before model is estimated.
- ...
- Other arguments passed to
`auto.arima`

when selecting p and q.

##### 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`

.

##### 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.

##### 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

##### Examples

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

*Documentation reproduced from package forecast, version 3.22, License: GPL (>= 2)*