Applying AIC to determine appropriate ARIMA model

Question

If I somehow know that a variable $Y$ is explained by an ARIMA process, and I know the number of times that the observations must be "differenced" to obtain a stationary series, I have read that it is appropriate to use AIC to determine the number of regressor variables in the model.

The formula for AIC is $AIC=2p + 2ln(L)$, where $p$ is the total number of regressors, and $L$ is the maximum of the likelihood function, and the best number of regressors is the one which minimizes the AIC.

My question is, if I determine for example that AIC is lowest when $p=5$, how do I know which of these five regressors are lagged $y$ variables, and which of the five regressors are lagged error terms?

Answer 1

AIC is used to compare particular models against each other. How could you even arrive to the conclusion that AIC lowers at p=5 without actually fitting the model that gives such low AIC?

Also, I would not use AIC as the only criterion to determine model selection. If you already know that your series follows an ARIMA process, just pick the simplest model that leaves no significant autocorrelations on its residuals (you may also want to check the squared residuals to confirm no heteroskedasticity)