Regularized Random Subspace Regressions

We propose a new class of Regularized Random Subspace Regressions (RRSRs) that combine the variance reduction benefits of regularized estimators with the non-linearities of random subspace ensembles. The approach introduces regularization in the selection of predictor subspaces, coefficient estimation within each subspace, or in both, yielding a flexible family of models that nest both RSR and standard penalized regressions as special cases. Using the FRED-MD database as a large predictor space, we show that RRSRs consistently outperform traditional RSR and several widely used econometric and machine learning benchmarks when forecasting four key macroeconomic indicators: inflation, output, unemployment, and the federal funds rate. The most systematic gains arise from the double-regularized specification, underscoring the value of applying shrinkage jointly to subspace selection and coefficient estimation.