Supervised Dynamic PCA: Linear Dynamic Forecasting with Many Predictors

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 rescale each predictor according to their significance in forecasting the targeted variable in a dynamic fashion, and a PCA is then applied to a rescaled and additive panel, which establishes a connection between the predictability of the PCA factors and the target variable. We also propose to use penalized methods such as the LASSO 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. An 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

本文提出一种新颖的动态预测方法，当存在大量预测变量时，采用新型有监督主成分分析（Supervised Principal Component Analysis, PCA）。该方法通过对预测变量及其滞后值进行缩放与组合，有效搭建起预测变量与目标变量间的关联，进而实现高效的动态预测。与传统扩散指数法不同——传统扩散指数法在执行主成分分析前，并未学习预测变量与目标变量间的关联——我们首先依据各预测变量在动态预测目标变量中的显著性对其进行重新缩放，随后对缩放后的加性面板数据执行主成分分析，由此建立了PCA因子的可预测性与目标变量之间的联系。我们还提出采用套索回归（LASSO）等惩罚类方法，筛选出预测能力优于其他因子的显著因子。理论层面，我们证明了在温和条件下，所提出的估计量具有一致性，且在预测任务中优于传统方法。我们开展了大量模拟实验，验证了所提方法可获得令人满意的预测结果，且相较于多数采用传统PCA的现有方法表现更优。通过利用大量预测变量预测美国宏观经济变量的实例可见，本文方法在实际应用中优于多数现有同类方法。本文的补充材料可在线获取，其中包含了可用于复现该研究的标准化材料说明。