Scaled PCA: A New Approach to Dimension Reduction
提出缩放主成分分析（sPCA），通过按预测能力缩放变量来改进传统PCA，在预测中表现更优，适合宏观经济预测等场景。
This paper proposes a novel supervised learning technique for forecasting: scaled principal component analysis (sPCA). The sPCA improves the traditional principal component analysis (PCA) by scaling each predictor with its predictive slope on the target to be forecasted. Unlike the PCA that maximizes the common variation of the predictors, the sPCA assigns more weight to those predictors with stronger forecasting power. In a general factor framework, we show that, under some appropriate conditions on data, the sPCA forecast beats the PCA forecast, and when these conditions break down, extensive simulations indicate that the sPCA still has a large chance to outperform the PCA. A real data example on macroeconomic forecasting shows that the sPCA has better performance in general. This paper was accepted by Kay Giesecke, Management Science Special Section on Data-Driven Prescriptive Analytics.