I've got an ARIMA(1,1,4) model using external regressor with acceptable output but I'm not able to reproduce it outside the R.
this is the result for the model:
Coefficients: ar1 ma1 ma2 ma3 ma4 XRegressor[1:39, ]_coeff 0.9500 -1.0202 0.3977 -0.8283 0.6030 0.0084 s.e. 0.1106 0.1999 0.1953 0.2003 0.1526 0.0059 sigma^2 estimated as 9619542: log likelihood=-360.56 AIC=735.11 AICc=738.84 BIC=746.57
The formula I'm using is as follows:
x(t) = x(t-1)(1+ar1) - ar1*x(t-2) + XRegressor[1:39, ]_coeff* [xreg(t) - (1+ar1)*xreg(t-1) + ar1*xreg(t-2)] + ma1*e(t-1) + ma2*e(t-2) + ma3*e(t-3) + ma4*e(t-4)
I'm using residuals as error term in above formula. I could get right result in one step ahead forecast and for further steps, I won't have residuals to substitute in formula. Even by deleting MA part from model, it's not working. Do I miss something here? Can I say by deleting MA part, I'm erasing residual effects?
Thanks a lot for your help in advance.