I have been wondering, is there any case in which AIC should be avoided as the evaluation metric? I cannot really find anything but for the advantages - what about the disadvantages? I'm mostly interested in time series models - assuming it changes anything.
AIC is asymptotically identical to leave-one-out cross-validation. Thus, you should use it any time you would use CV to select your model, which is mainly when you want to minimise predictive error.
The disadvantage is that in a limited data situation, AIC will not select the causal model, and in the large-data limit, AIC will select more complicated models than BIC, and is not necessarily asymptotically consistent if the true model is in the set.
I would say the bottomline is that AIC is a good criteria if you want to minimise predictive error in a data-limited situation.