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

Zhentao Shi, Liangjun Su and Tian Xie
Additional contact information
Zhentao Shi: Georgia Institute of Technology and Chinese University of Hong Kong
Liangjun Su: Tsinghua University
Tian Xie: Shanghai University of Finance and Economics

The Review of Economics and Statistics, 2025, vol. 107, issue 2, 523-538

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.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1162/rest_a_01261
Access to PDF is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tpr:restat:v:107:y:2025:i:2:p:523-538

Ordering information: This journal article can be ordered from
https://mitpressjour ... rnal/?issn=0034-6535

Access Statistics for this article

The Review of Economics and Statistics is currently edited by Pierre Azoulay, Olivier Coibion, Will Dobbie, Raymond Fisman, Benjamin R. Handel, Brian A. Jacob, Kareen Rozen, Xiaoxia Shi, Tavneet Suri and Yi Xu

More articles in The Review of Economics and Statistics from MIT Press
Bibliographic data for series maintained by The MIT Press ().