Comparison between TS models - is AIC_C or ACF/PACF analysis better to choose by? When building a model for a time series, I have received different recommendations -
One is to choose the model with the smallest AIC_C value, e.g. do an initial ACF/PACF analysis of the raw data to get an idea of what kind of model to go for, and then choose between candidate models by going for the one that minimises the AIC_C value. This approach is described here.
Another is to choose the model with the nicest ACF and PACF (i.e. no significant spikes, not with any obvious structure and following a normal distribution). In this approach, remove one kind of variance at a time, look at the ACF/PACF again, remove another kind of variance based on that and keep going until the ACF/PACF can't be improved any further. Use likelihood ratio tests to decide between models if the eyes can't detect the difference.
I have seen many examples where the one of these approaches chooses one model and the other chooses another model.
Is it possible to generally say which is better?
(I'm using R for analysis if that's of any interest)
EDIT: In my present analysis, the AICc approach chooses an ARIMA(1,0,0)(0,1,0)[12] model, whereas the ACF/PACF approach chooses an ARIMA(0,1,0)(1,0,0)[12] model. The AICc model has an AICc of 307.21 and a standard error of 0.142, whereas the ACF/PACF model has an AICc of 463.99 and a standard error of 0.0704. 
 A: The problem with AIC-based relationships is that they premise : 1) no pulses/level shifts/seasonal pulses/local time trends exist in the data because if they did ( and they always do) the AIC statistics are meaningless because they premise a model free of that structure; 2) that there is constant error variance and constant parameters in the premised model:  and 3) that there are no missing lags in the premised model. These assumptions do not hold for a data-based approach as the Gaussian Violations can all be tested and rectified by possible model augmentation or simplification. The whole idea of empirically identifying a useful model is to follow the concepts of the General Linear Model in forming both memory and any needed deterministic structure while encoding any needed transformations such as power transforms/weighted  least squares and arch/garch .
the big lie in econometrics is that you are supposed to know/guess your model before you observed the data. This of course could lead to throwing out the observed data until you find data that conforms to your pre-specified model. … just teasing here. The econometrician is not supposed to discover new structure but in effect when you delete specified structure you are changing the model. The pure empiricist starts with no model and carefully both augments and refines the current candidate until all coefficients are statistically significant and that there is no evidented structure in the model’s residuals. 
The software that I use allows not only the pure theoretical specification and the pure empirical approach BUT the middle ground where a pre-specified/theoretical model is used as the Starting Model 
A reasonable place to start are the flow diagrams that I prepared using sound exploratory techniques http://www.autobox.com/cms/index.php/blog/entry/build-or-make-your-own-arima-forecasting-model  in response to a query much like the one from @Richard Hardy.
A: It's a pretty general question and any simple answer will not be completely satisfactory. However...
If you have a number of candidate models, choose by AICc. This will give you the best model (in a certain sense, defined by the AICc criterion) available given the data sample you have. Even though noise may dominate over the signal in your data (which is a popular criticism), still AICc will give you the best there is in terms of this particular criterion.
Meanwhile, choosing by ACF/PACF would mean data mining. Choosing a model from a pool of candidate models by looking for a desired feature (like a nice ACF/PACF plot) is not the same as first choosing a model and then checking whether it has the desired feature. It is a bit like saying "I will toss a coin; if it comes heads up, I will go do the washing up; if tails, I will watch TV. <...toss...> Oops, it came heads up... I better try again... Oh no, heads up again! Try once more... Hooray, now it's tails! I can go watch TV!" You only trick yourself this way.
