[R] arima function - estimated coefficients and forecasts

Richard A. Bilonick rab at nauticom.net
Wed Apr 16 23:15:53 CEST 2003

I'm using the arima function to estimate coefficients and also using 
predict.Arima to forecast. This works nicely and I can see that the 
results are the same as using SAS's proc arima.

I can also take the coefficent estimates for a simple model like 
ARIMA(2,1,0) and manually compute the forecast. The results agree to 5 
or 6 decimal places. I can do this for models with and without means 
(i.e., using the include.mean argument).

When I include an exogenous variable using the xreg argument, I can't 
manually reproduce the forecast I get when using predict.Arima with the 
newxreg argument, even with just one exogenous variable with an AR(1) 
model for the response.  There does not appear to be any information in 
the arima help file explaining the model when xreg is used. I would have 
thought it was as simple as including an extra term containing the 
product of the coefficient and the value of the exogenous variable. Yet 
I can't manually reproduce the forecast. The manual forecasts seems to 
be off by a constant and a scale factor but I can't for the life of me 
see how I can fix this. Could someone point me in the right direction?

Rick B.

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