This paper proposes a novel dynamic forecasting method using a new supervised Principal Component Analysis (PCA) when a large number of predictors are available. The new supervised PCA provides an effective way to bridge the gap between predictors and the target variable of interest by scaling and combining the predictors and their lagged values, resulting in an effective dynamic forecasting. Unlike the traditional diffusion-index approach, which does not learn the relationships between the predictors and the target variable before conducting PCA, we first re-scale each predictor according to their significance in forecasting the targeted variable in a dynamic fashion, and a PCA is then applied to a re-scaled and additive panel, which establishes a connection between the predictability of the PCA factors and the target variable. Furthermore, we also propose to use penalized methods such as the LASSO approach to select the significant factors that have superior predictive power over the others. Theoretically, we show that our estimators are consistent and outperform the traditional methods in prediction under some mild conditions. We conduct extensive simulations to verify that the proposed method produces satisfactory forecasting results and outperforms most of the existing methods using the traditional PCA. A real example of predicting U.S. macroeconomic variables using a large number of predictors showcases that our method fares better than most of the existing ones in applications. The proposed method thus provides a comprehensive and effective approach for dynamic forecasting in high-dimensional data analysis.

翻译：本文提出了一种当存在大量预测因子时，利用新型监督主成分分析（PCA）的动态预测方法。该监督PCA通过缩放和组合预测因子及其滞后值，有效弥合了预测因子与目标变量之间的差距，从而实现高效的动态预测。与传统的扩散指数方法在进行PCA前不学习预测因子与目标变量关系不同，我们首先根据每个预测因子在动态预测目标变量中的重要性对其进行重新缩放，随后对缩放后的加性面板应用PCA，从而建立了PCA因子可预测性与目标变量之间的关联。此外，我们还提出使用LASSO等惩罚方法筛选具有超强预测能力的显著因子。理论上，我们证明了在温和条件下，我们的估计量具有一致性，且预测效果优于传统方法。通过大量仿真验证，该方法能产生令人满意的预测结果，并优于多数基于传统PCA的现有方法。利用大量预测因子预测美国宏观经济变量的实际案例表明，该方法在实际应用中优于大多数现有方法。因此，本文提出的方法为高维数据分析中的动态预测提供了一种全面且有效的解决方案。