Scaled PCA: A New Approach to Dimension Reduction

Abstract

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 weights 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 if 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.

Keywords: Forecasting, PCA, Big Data, Machine Learning, Supervised Learning

JEL Classification: C22, C23, C53