Regularized Random Subspace Regressions

Yilin Xiao and Jamie L. Cross

CAMA Working Papers from Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University

Abstract: 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.

Keywords: big data; forecasting; machine learning; model averaging; random subspace; regularization (search for similar items in EconPapers)
JEL-codes: C22 C53 C55 E37 (search for similar items in EconPapers)
Pages: 33 pages
Date: 2026-02
New Economics Papers: this item is included in nep-ecm
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https://crawford.anu.edu.au/sites/default/files/2026-02/13_2026_Xiao_Cross.pdf (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:een:camaaa:2026-13

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