R: Fit a fractionally differenced ARFIMA model

arfima {forecast} | 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, 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.

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

### Examples

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

[Package forecast version 8.4 Index]