"AIC is used to evaluate ARIMA commonly. AIC criteria are only used to compare nested models. This means that the smaller model (e.g., 0, 1, 0)must be a subset of the larger model (1, 1, 0). The tests are not legitimately used to compare, for example, (1, 0, 1) and (0, 1, 0). And they could not be used to compare models in which a different value of d is generated by coding the IV differently."

I do not have a link (I gathered this many years ago).