Solving the Forecast Combination Puzzle
解释预测组合之谜AI 解读 ↓
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解释预测组合之谜
- 研究问题
- 为何优化权重的预测组合常未胜过等权组合，这一现象是否源于组合估计方式及预测精度检验的尺寸和功效问题？
- 方法与思路
- 作者分析预测精度检验统计量的非标准渐近分布，并讨论可行时采用更有效率的组合估计，涵盖目标泛函与预测密度。
- 材料陈述的贡献
- 摘要称常用检验可能缺乏尺寸控制且功效低，从而偏向简单组合；更有效率的估计可避免所讨论的低功效问题。
- 阅读关注点
- 应核对非标准极限分布出现的条件、可行的高效估计策略，以及金融收益示例如何区分预测表现和检验判断。
- 阅读边界
- 所据为 arXiv 预印本，同行评审或期刊接收未核实；摘要未说明具体分布与效率条件，不能推断优化组合普遍胜出。
原文摘要
We demonstrate that the forecasting combination puzzle is a consequence of the methodology commonly used to produce forecast combinations. By the combination puzzle, we refer to the empirical finding that predictions formed by combining multiple forecasts in ways that seek to optimize forecast performance often do not out-perform more naive, e.g. equally-weighted, approaches. In particular, we demonstrate that, due to the manner in which such forecasts are typically produced, tests that aim to discriminate between the predictive accuracy of competing combination strategies can have low power, and can lack size control, leading to an outcome that favours the naive approach. We show that this poor performance is due to the behavior of the corresponding test statistic, which has a non-standard asymptotic distribution under the null hypothesis of no inferior predictive accuracy, rather than the {standard normal distribution that is} {typically adopted}. In addition, we demonstrate that the low power of such predictive accuracy tests in the forecast combination setting can be completely avoided if more efficient estimation strategies are used in the production of the combinations, when feasible. We illustrate these findings both in the context of forecasting a functional of interest and in terms of predictive densities. A short empirical example {using daily financial returns} exemplifies how researchers can avoid the puzzle in practical settings.