# [R] Arima with an external regressor

Prof Brian Ripley ripley at stats.ox.ac.uk
Mon Sep 1 16:19:05 CEST 2003

```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

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

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