Why can the aggregated prediction of two bad models be better than the one two very good models? I am modeling two separated processes (e.g., number of events A and B). As jointly modeling both processes is not possible, I estimate for each process three different models.
When I look at the three models for process A, there is a clear "winner" and a clear "loser" in terms of predictive performance. The same applies to process B.
In order to come up with an "aggregated prediction", I sum the predictions of the individual models:

*

*First, I sum the predictions of the two best models for process A and B.

*Then, I do the same with the two "loser models".

*Finally, I look at the MAEs for the "aggregated predictions" of both alternatives.

=> Surprisingly the MAE is lower/better for the aggregated prediction of the two "loser models".
Apparently, their individual errors cancel out when combing the predictions for the two processes.
I suppose this should be a phenomenon that has been discussed previously in literature (when 2 processes are estimated separately, but subsequently, an aggregated prediction is derived).
Is there a term for this in statistics?

This is explained by "independence of the errors". If two models have independent error terms, they can cancel each other out, and the result may be better predictions. If the errors are dependent, the predictions will not be improved (both models make the same mistakes).
Independent errors are more likely with completely different models, for example, based on different columns, or different training samples, or using a different algorithm.
A random forest combines many different trees (these are losers by themselves), where all of them are grown on different subsets of columns and features. This way, the errors will be more or less independent and the result is an accurate model.
Combining different algorithms (a random forest with a neural network for example) is known as stacking.
