I have a data set of weekly sales for a range of stores (all belonging to one company). I am trying to predict weekly/monthly use of several ingredients in the individual stores. The choice for what type of model to use seems to be between Holt Winter (or state space models more generally) and the class of ARIMA models.
I have made a range of analyses testing which type works best over the entire dataset. That is, I have for example looked at what model describe any given series best and then counted which describes the most series best. This has been done using MSE, MAPE and other measures.
However, I am not sure whether I should simply determine which model is best for any given individual series and then use that. The reasons I haven't done that is because it seems more intuitive to use the same model for all series.
And so my question is, is there any particular theoretical or practical reason, why I would want to choose one method or the other?