R help - Sep 2003 - Arima with an external regressor

It's stated on the help page, and it is neither.

Maybe SAS does use `residuals' but `errors' as on the R page is the 
correct term.

What was the problem with doing ?arima?  Unlike SAS, you have the source 
code to read too.

On Mon, 1 Sep 2003, Eric ESPOSITO wrote:
> 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
> function
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

Hello,
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
function

Thank you,
Eric Esposito