[R] Forecasting by using ARFIMA(0, d, 0) models in R

ecarreno at unsl.edu.ar
Thu, 22 Jan 2009 04:01:17 -0000

Hello. I'm trying to make k-step-ahead forecasts using ARFIMA(0, d, 0)
models by taking the first T+k-1 coefficients in the binomial expansion of
(1-B)^d, regarding (1-B)^d x(T+k)  as an  AR(T+k-1) on  x(T+k), where x(T)
is the series value at time T  and k = 1, 2, 3,
. That is, I forecast the
series k values forward using the first T+k-1 coefficients in the binomial
expansion of (1-B)^d as the coefficients in an AR(T+k-1). This method is
usually referred to as the truncation method. For example:

(1-B)^d x(T) = x(T) + c1 x(T-1) + c2 x(T-2)
 = whiteNoise

then,

x(T) = -c1 x(T-1) - c2 x(T-2) -  c3 x(T-3) -
 + WhiteNoise

and the AR(T) is:

x(T+1) =- c1 x(T) - c2 x(T-1)  - c2 x(T-2) -
 - cT x(1)

The forecasts are computed recursively like in an AR model.

There does not exist a built-in function to forecast with ARFIMA(0, d, 0)
models, then:
How can I implement this by using R?
How can I get the first T coefficients in the binomial expansion (c1,
, cT)?

Some software packages include both the best linear predictor (using the
Durbin-Levinson algorithm) and the truncation method. The best linear
predictor is used to forecast stationary time series and the truncation
method (also know as Naive forecasts) is used to forecast non- stationary
series. Then, an R built-in implementation should include both methods.
Let me know what you think on this.

Thanks in advance, any help will be appreciated.
Emiliano.