Mining Big Data Using Parsimonious Factor, Machine Learning, Variable Selection and Shrinkage Methods

Abstract

A number of recent studies in the economics literature have focused on the usefulness of factor models in the context of prediction using big data. We add to this literature by analyzing whether big are useful for modelling low frequency macroeconomic variables such as unemployment, inflation and GDP. In particular, we analyze the predictive benefits associated with the use of principal component analysis (PCA), independent component analysis (ICA), and sparse principal component analysis (SPCA). We also evaluate machine learning, variable selection and shrinkage methods, including bagging, boosting, ridge regression, least angle regression, the elastic net, and the non-negative garotte. Our approach is to carry out a forecasting horse-race using prediction models constructed using a variety of model specification approaches, factor estimation methods, and data windowing methods, in the context of the prediction of 11 macroeconomic variables relevant for monetary policy assessment. In many instances, we find that various of our benchmark models, including autoregressive (AR) models, AR models with exogenous variables, and (Bayesian) model averaging, do not dominate specifications based on factor-type dimension reduction combined with various machine learning, variable selection, and shrinkage methods (called models). We find that forecast combination methods are mean square forecast error (MSFE) best for only 3 of 11 variables when the forecast horizon, h=1, and for 4 variables when h=3 or 12. Additionally, non-PCA type factor estimation methods yield MSFE-best predictions for 9 of 11 variables when h=1, although PCA dominates at longer horizons. Interestingly, we also find evidence of the usefulness of combination models for approximately 1/2 of our variables, when h>1. Most importantly, we present strong new evidence of the usefulness of factor based dimension reduction, when utilizing big for macroeconometric forecasting.