ecarreno at unsl.edu.ar
2009-Jan-22 04:01 UTC
[R] Forecasting by using ARFIMA(0, d, 0) models in R
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.