I used R forecast package and the best fit resulted in (1,1,2)(1,0,1) [7] with one regressor variable (X). I built the equation as follow:

# (1- ar1**B)*(1 - sar1**B7)*(1 - B)*Yt = (1 + ma1**B - ma2**B2)*(1 - sma1**B7)*Et

# thus: 

# Yt = ar1*(Yt-1) + Yt-1 - ar1*(Yt-2) + sar1*(Yt-7) + ar1*sar1*(Yt-8) - sar1*(Yt-8) + ar1*sar1*(Yt-9) + ma1*(Et-1) - ma2*(Et-2) - sma1*(Et-7) + ma1*sma1*(Et-8 ) + ma2*sma1*(Et-9) + xreg*(Xt)

1) How R computes the error term (Et) for the first seven fitted values?

Thank you!

  • $\begingroup$ I don't understand. Do you want the fitted and residual components of each observation? If so, they are available in the model. $\endgroup$ – user2974951 Aug 21 at 10:53
  • $\begingroup$ I have the mathematical structure of the model "(2,1,0)(0,0,2) [7]" and from the equation I estimated the predicted values "Y(t)", but how can I know the value of "e(t)" without looking the values giving by the R program. I would like to do it manually $\endgroup$ – ChrisGila Aug 21 at 10:56
  • $\begingroup$ The predicted value ($\hat{y}=\bar{y}+\epsilon$) is the fitted value in this case, unless you applied some sort function to the values beforehand. $\endgroup$ – user2974951 Aug 21 at 11:04

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