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ℓ2-Relaxation: With Applications to Forecast Combination and Portfolio Analysis

Author

Listed:
  • Zhentao Shi

    (Georgia Institute of Technology and Chinese University of Hong Kong)

  • Liangjun Su

    (Tsinghua University)

  • Tian Xie

    (Shanghai University of Finance and Economics)

Abstract

We propose ℓ2-relaxation, which is a novel convex optimization problem, to tackle a forecast combination with many forecasts or a minimum variance portfolio with many assets. ℓ2-relaxation minimizes the squared Euclidean norm of the weight vector subject to a set of relaxed linear inequalities to balance the bias and variance. It delivers optimality with approximately equal within-group weights when latent block equicorrelation patterns dominate the high-dimensional sample variance-covariance matrix of the individual forecast errors or the assets. Its wide applicability is highlighted in three real data examples in microeconomics, macroeconomics, and finance.

Suggested Citation

  • Zhentao Shi & Liangjun Su & Tian Xie, 2025. "ℓ2-Relaxation: With Applications to Forecast Combination and Portfolio Analysis," The Review of Economics and Statistics, MIT Press, vol. 107(2), pages 523-538, March.
    • Handle: RePEc:tpr:restat:v:107:y:2025:i:2:p:523-538
    DOI: 10.1162/rest_a_01261
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