On the Forecast Combination Puzzle

TL;DR

This paper investigates why simple averaging often outperforms complex forecast combining methods, identifies key factors causing this puzzle, and proposes an adaptive multi-level strategy to improve forecast combination performance.

Contribution

It introduces a new perspective on the forecast combination puzzle by distinguishing combining scenarios and proposes an adaptive method to address the issue.

Findings

Simple average is often more robust than complex methods.

The proposed multi-level AFTER strategy effectively adapts to different scenarios.

Simulations and real data confirm the strategy's ability to mitigate the puzzle.

Abstract

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.