# Why only full ARIMA models in auto.arima?

It seems that the auto.arima function in the "forecast" package in R only considers full ARIMA models. By "full" I mean that if an AR lag $k$ is included, AR lag $j$ will also be included for $k>1$, $0<j<k$ (and the same with MA in place of AR). This was claimed here by the author of the auto.arima function himself.

I am interested in non-full (restricted) ARIMA models, e.g. an AR(2) model where the first AR lag is restricted to zero: $x_t=\varphi_2 x_{t-2}+\varepsilon_t$.

Question 1: Is there a good theoretical reason for not considering the non-full ARIMA models?

Question 2: Is there a good practical reason for not considering the non-full ARIMA models? (Besides the argument of high computational burden if all sub-models within given maximum AR and MA orders are to be estimated.)

• I think the answer to the linked question is a bit misleading because (and the answer even states this) you can fit non-full ARIMAs using the fixed parameter. – bdeonovic Oct 24 '14 at 13:35
• @Benjamin: Thanks, I noticed that. However, it is a bit tedious (although certainly possible) to program a search over all subset models. I wonder why it has not been done so far and is not an option in auto.arima(). Perhaps there are good reasons? – Richard Hardy Oct 24 '14 at 13:41