# 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(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. 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.

- x
Deprecated. Included for backwards compatibility.

- …
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

```
# NOT RUN {
library(fracdiff)
x <- fracdiff.sim( 100, ma=-.4, d=.3)$series
fit <- arfima(x)
tsdisplay(residuals(fit))
# }
```

*Documentation reproduced from package forecast, version 8.9, License: GPL-3*