标题： 预报线性增强投影（FLAP）：减少预报误差方差的免费午餐 显示英文标题

标题： Forecast Linear Augmented Projection (FLAP): A free lunch to reduce forecast error variance

摘要： 一种新的预报线性增强投影（FLAP）方法被引入，该方法在不引入偏差的情况下减少了任何无偏多变量预报的预报误差方差。 该方法首先构建新的成分序列，这些序列为原始序列的线性组合。 然后，为原始序列和成分序列生成预测。 最后，将完整的预测向量投影到一个线性子空间上，在该子空间中组合权重所隐含的约束成立。 证明了随着成分数量的增加，预报误差方差的迹非递增，并建立了使其严格递减的温和条件。 还表明，所提出的方法在所有线性投影方法中实现了最大的预报误差方差减少。 通过仿真和基于澳大利亚旅游业及FRED-MD数据的两个实证应用验证了理论结果。 值得注意的是，使用FLAP结合主成分分析（PCA）来构造新序列会导致显著的预报误差方差减少。 显示英文摘要

摘要： A novel forecast linear augmented projection (FLAP) method is introduced, which reduces the forecast error variance of any unbiased multivariate forecast without introducing bias. The method first constructs new component series which are linear combinations of the original series. Forecasts are then generated for both the original and component series. Finally, the full vector of forecasts is projected onto a linear subspace where the constraints implied by the combination weights hold. It is proven that the trace of the forecast error variance is non-increasing with the number of components, and mild conditions are established for which it is strictly decreasing. It is also shown that the proposed method achieves maximum forecast error variance reduction among linear projection methods. The theoretical results are validated through simulations and two empirical applications based on Australian tourism and FRED-MD data. Notably, using FLAP with Principal Component Analysis (PCA) to construct the new series leads to substantial forecast error variance reduction.