# ARIMA and external regressors in SAS and R

So I remember reading somewhere that when we have external regressors, auto.arima cannot make correct predictions for the order of difference for either seasonality or the main time series itself (correct me if I'm wrong!)

Now, I'd like to know whether we'd need to difference the external regressors as well? Also, in the case of having external regressors (a few time series and a few dummies for seasonal patterns in those time series), can auto.arima even calculate the optimal MA and AR?

Also, I have weekly seasonality as well as quarterly and yearly seasonality; since I can't specify that many seasonalities in auto.arima, I'm inputting a lot of dummy variables for quarters and months; will that yield mathematically correct results?

Further, for those of you who have worked with SAS, when using the forecast procedure and estimating the input variables (the external regressors), does it automatically calculate the MA and AR for each external regressor?

auto.arima can select the order of differencing automatically, and make appropriate forecasts taking account of these differences. It can also include regressors via the xreg argument, and select the appropriate model order taking account of the regressors. If you include regressors, these will be differenced along with the response variable as part of the estimation. You do not have to difference them first. Please read http://otexts.com/fpp/9/1 on how it works.

When you refer to the "MA and AR for each external regressor", I assume you must be thinking of a transfer function model. This is not the model that is fitted using auto.arima. Please see http://robjhyndman.com/hyndsight/arimax/ for a discussion of the various models involving ARIMA like terms and regressors.

• Thank you very much Dr. Hyndman! I have a few more questions and I would really appreciate it if you could address them. One of my external regressors is non-stationary and seasonal and the other is not. Can I input these two variables in auto.arima? Specially with the seasonal regressor, I had no success, so I used dummy variables for days and months, and instead of the seasonal variable I used the seasadj() function to extract the trend, which worked. Also, will auto.arima take the lags of external regressors into consideration, or is there any way to address this manually? – user2370334 May 20 '13 at 11:44
• For example surges in advertising spend (external regressor) that cause an increase in sales but with a few days lag. Further, auto.arima will not work if the number of rows in the main series is not equal to the number of rows in the xreg series. Would that mean that if differenced, they will be differenced with the same order, and the dummy variable will also be differenced? Thank you very much in advance, Farhad – user2370334 May 20 '13 at 11:45
• Please construct a new question. Comments are no place for extended consultations. – Rob Hyndman May 20 '13 at 12:42
• Thank you Dr. Hyndman. I created a new question! Thanks. – user2370334 May 20 '13 at 13:19