Forecasting Near-equivalence of Linear Dimension Reduction Methods in Large Panels of Macro-variables

In an extensive pseudo out-of-sample horserace, classical estimators (dynamic factor models, RIDGE and partial least squares regression) and the novel to forecasting, Regularized Sliced Inverse Regression, exhibit almost near-equivalent forecasting accuracy in a large panel of macroeconomic variables across targets, horizons and subsamples. This finding motivates the theoretical contributions in this paper. Most widely used linear dimension reduction methods are shown to solve closely related maximization problems with solutions that can be decomposed in signal and scaling components. They are organized under a common scheme that sheds light on their commonalities and differences as well as on their functionality. Regularized Sliced Inverse Regression delivers the most parsimonious forecast model and obtains the greatest reduction of the complexity of the forecasting problem. Nevertheless, the study’s findings are that (a) the intrinsic relationship between forecast target and the other macroseries in the panel is linear and (b) targeting contributes in reducing the complexity of modeling yet does not induce significant gains in macroeconomic forecasting accuracy.