# arfima: Fit a fractionally differenced ARFIMA model In forecast: Forecasting Functions for Time Series and Linear Models

 arfima R Documentation

## 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,
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.

### 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).

`fracdiff`, `auto.arima`, `forecast.fracdiff`.

### Examples

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

```

forecast documentation built on July 25, 2022, 5:05 p.m.