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 maximum likelihood estimation based on
Haslett and Raftery (1989) to estimate the parameters including d.
Usage
arfima(x, drange = c(0, 0.5), ...)
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.
...
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.
References
J. Haslett and A. E. Raftery (1989) Space-time Modelling with Long-memory Dependence: Assessing
Ireland's Wind Power Resource (with discussion); Applied Statistics38, 1-50.
Hyndman, R.J. and Khandakar, Y. (2008) "Automatic time series forecasting: The forecast package for R",
Journal of Statistical Software, 26(3).