Supervised Kernel Principal Component Analysis for Forecasting

Principal component analysis (PCA) is a versatile tool for dimension reduction with many applications in finance, economics, and machine learning. This paper proposes a new approach to improving the forecasting ability of the Principal Components (PCs) of observed high-dimensional predictors in a factor-augmented forecasting framework. The approach is carried out in a three-step procedure, where we first perform a nonparametric kernel regression of the target variable on each predictor to obtain a new high-dimensional predictor vector formed by stacking all estimated kernel regression functions, we then extract PCs from these new predictors using PCA, and finally, we employ the extracted PCs as predictors to forecast the target variable. A real example on macroeconomic forecasting is analyzed and numerical results show that the proposed kernel PCA can outperform some commonly used forecasting approaches in out-of-sample prediction.