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) model, whereas the ACF/PACF approach chooses an ARIMA(0,1,0)(1,0,0) 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.