标题： 监督动态PCA：具有许多预测变量的线性动态预测 显示英文标题

标题： Supervised Dynamic PCA: Linear Dynamic Forecasting with Many Predictors

摘要： 本文提出了一种新的动态预测方法，当存在大量预测变量时，该方法使用一种新的监督主成分分析（PCA）。新的监督PCA通过缩放和组合预测变量及其滞后值，提供了一种有效的方法来弥合预测变量与目标变量之间的差距，从而实现有效的动态预测。与传统的扩散指数方法不同，传统方法在进行PCA之前不学习预测变量与目标变量之间的关系，我们首先根据预测变量在动态预测目标变量中的重要性重新缩放每个预测变量，然后对重新缩放和加法面板进行PCA，这建立了PCA因子的可预测性与目标变量之间的联系。此外，我们还建议使用惩罚方法，如LASSO方法，来选择具有优于其他因素的预测能力的重要因素。理论上，我们证明了我们的估计量是一致的，并且在一些温和条件下，其预测效果优于传统方法。我们进行了广泛的模拟，以验证所提出的方法产生了令人满意的预测结果，并且在使用传统PCA时优于大多数现有方法。一个使用大量预测变量预测美国宏观经济变量的实际例子展示了我们的方法在应用中比大多数现有方法表现更好。因此，所提出的方法为高维数据分析中的动态预测提供了一个全面而有效的方法。 显示英文摘要

摘要： 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.