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"), ...)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. Ifestim=="mle", then the ARMA parameters are calculated using full MLE via thearima - ...
- Other arguments passed to
auto.arimawhen 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 thefracdiffdocumentation. A few additional objects are added to the list includingx(the original time series), and theresidualsandfittedvalues.
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))