# comparing ARIMA and AR with external regressor

Consider the following models fitted to the same time series:

• ARIMA(0,1,1)

• ARIMA(1,0,0) (that is, AR(1)) with an external regressor

Can I use the AIC (or any other information criteria) to decide which one is better?

I know that in order to use the AIC to compare models these have to be fitted to the same dataset. Does this hold when I = 1? Does this hold when I use an external regressor in my model?

• No, the AICs on differenced model cant be compared to AR Jul 21, 2015 at 15:20
• Thanks! Is there any other way I can compare these models then? Jul 21, 2015 at 15:25

You could go for $R^2$ like measure called FVU. Make sure you apply it on the dependent variable itself, not the differences. This is a "mechanical" approach. I'd hold off on this one though.
• Thank you for your answer, if I understand you think that $R^2$ like measures wouldn't be good on this case as well, is that right? I'll take a look at the autoregressive coefficients and residuals... I'm aware that comparing $I = 1$ with $I = 0$ isn't ideal, but in my specific case I'm getting different results depending on which unit root test I use, so I can't quite accept / reject the presence of an unit root... Jul 23, 2015 at 13:41
• You don't have $R^2$ for MA models, generally, they can't be estimated by linear regression function. Jul 23, 2015 at 14:16