Scaled PCA: A new approach to dimension reduction

• Main Authors: HUANG, Dashan, JIANG, Fuwei, LI, Kunpeng, TONG, Guoshi, ZHOU, Guofu
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2022
• Subjects: Forecasting; PCA; Big Data; Dimension Reduction; Machine Learning; Management Sciences and Quantitative Methods
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/6924; https://ink.library.smu.edu.sg/context/lkcsb_research/article/7923/viewcontent/SSRN_id3358911.pdf
• Institution: Singapore Management University

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.