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Regularized Random Subspace Regressions

Author

Listed:
  • Yilin Xiao
  • Jamie L. Cross

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.

Suggested Citation

  • Yilin Xiao & Jamie L. Cross, 2026. "Regularized Random Subspace Regressions," CAMA Working Papers 2026-13, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    • Handle: RePEc:een:camaaa:2026-13
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    File URL: https://crawford.anu.edu.au/sites/default/files/2026-02/13_2026_Xiao_Cross.pdf
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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