I want to predict daily headcount in a given area. The area can be divided into several blocks. The blocks share very little similarity.
The question is, if I'm only interested in total daily headcount, then
Is 1 always better than 2, if so, why?
Your question belongs to a subject called "forecast aggregation". Whether it's better to forecast the aggregated quantity or aggregate the component forecasts?
There's substantial research in this area. You can look at this ECB paper, particularly the "literature review" section in it to see what others think about this subject.
My rule of thumb is that aggregating the component forecasts works better when you have an idea of how the components are correlated. In this case you could use vector models or copulas or similar tools to capture the correlations.
The aggregate forecast, on the other hand, suffers badly when the components have very different contribution to the aggregate across time.
No, 1 is NOT always better than 2. On the contrary, 2 is likely better than 1 most of the time (Not always!). The reason I say this is that you are able to forecast the individual differences in headcount for each of these individual sub blocks. In essence, you are able to isolate each sub block and forecast their change over time without regards to the other sub blocks. Then by aggregating each sub blocks forecasts into one forecast, you will capture the intricacies of all of the sub blocks of interest, which will likely result in a more accurate and meaningful forecast for the area as a whole.
An example where 2 would likely be better than 1 is as follows:
If everyone in sub block decided that it would be a good idea to start sacrificing each other for the good of the community, we would likely see declines in headcount over time.
In another sub block, there may be a movement towards healthier living (more exercise, eating more fruits and vegetables, etc.) we may see life expectancy start to increase over time, thus delaying expected drops in headcount.
If we forecasted these two populations together, we would not capture these individual effects within these two sub blocks, which would likely lead to less accurate forecasts in aggregate.
