[R] Arima with an external regressor

Eric ESPOSITO eric.esposito at gazdefrance.com
Mon Sep 1 17:03:55 CEST 2003

Does anybody know if the function arima with an external regressor (xreg)
applies the auto correlation on the dependant variable or on the residuals.
In comparison with SAS (proc autoreg), it seems that the auto correlation
applies on the residuals but i'd like to have the confirmation.

I want to estimate:
Y[t] = a[1]*X[t] + a[2] + E[t]
with E[t]=b[1]*E[t-1]

Should I use :
arima(Y, xreg=X, order=c(1,0,0))          or rather              arima(Y,
xreg=X, order=c(0,0,1))
And what is the exact equation of the estimating model:
Y[t] = a[1]*X[t] + a[2] + E[t] + b[1]*E[t-1]     or       Y[t] = a[1]*X[t]
+ a[2] + b[1]*E[t-1]
where a[1], a[2] and b[1] are the coefficients returned by the arima

Thank you,
Eric Esposito

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