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 nonlinearities 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.