Scaled PCA : A New Approach to Dimension Reduction

We propose a novel modification to the popular 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 predictors, our scaled PCA, sPCA, puts more weights on those predictors that have stronger forecasting power. Asymptotically, we provide a set of sufficient conditions under which the sPCA forecast outperforms the PCA and partial least squares (PLS) forecasts. Simulated and real data show that the sPCA forecast outperforms the PCA forecast in general, and performs similarly as, and in some cases better than, the PLS forecast