Forecasting economic time series in the presence of weak factors: Multiple supervised learning-based approach

This paper proposes an innovative supervised learning technique for dimension reduction and forecasting financial and macroeconomic time series in the presence of weak factors that can undermine the effectiveness of traditional Principal Component Analysis (PCA). This approach employs double or multiple supervised learning procedures and is termed ‘Supervised Scaled Principal Component Analysis’ (SsPCA). Initially, each predictor is scaled using its predictive slope on the target forecast variable, giving more weight to those with stronger predictive abilities and less to those with weaker ones. Subsequently, utilizing the scaled predictors, we intelligently identify the most informative subset for prediction. This involves iterative steps of supervised selection, factor extraction through PCA, and projection. The integration of a pre-selection step, aimed at choosing ‘targeted predictors’ before executing the SsPCA procedure, especially using soft thresholding of supervised learning methods like elastic net, significantly enhances the predictive capacity of SsPCA. Additionally, incorporating the possibility of non-linear relationships between predictors and factors often leads to supplementary improvements. Through extensive Monte Carlo simulation exercises, we find that our proposed SsPCA procedure consistently outperforms standard PCA. Real-world examples involving macroeconomic and financial asset pricing forecasting further suggest that SsPCA generally exhibits superior performance.