  It is often reported in forecast combination literature that a simple average
of candidate forecasts is more robust than sophisticated combining methods.
This phenomenon is usually referred to as the "forecast combination puzzle".
Motivated by this puzzle, we explore its possible explanations including
estimation error, invalid weighting formulas and model screening. We show that
existing understanding of the puzzle should be complemented by the distinction
of different forecast combination scenarios known as combining for adaptation
and combining for improvement. Applying combining methods without consideration
of the underlying scenario can itself cause the puzzle. Based on our new
understandings, both simulations and real data evaluations are conducted to
illustrate the causes of the puzzle. We further propose a multi-level AFTER
strategy that can integrate the strengths of different combining methods and
adapt intelligently to the underlying scenario. In particular, by treating the
simple average as a candidate forecast, the proposed strategy is shown to avoid
the heavy cost of estimation error and, to a large extent, solve the forecast
combination puzzle.

Methodology;Economics