forecast (version 3.08)

arfima: 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(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.

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

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