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L2-Relaxation: With Applications to Forecast Combination and Portfolio Analysis

Zhentao Shi, Liangjun Su, Tian Xie

arXiv 19 Oct 2020 · Econometrics · publishedThe Review of Economics and Statistics (2022) · 5 citations (OpenAlex)

arXiv:2010.09477 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper tackles forecast combination with many forecasts or minimum variance portfolio selection with many assets. A novel convex problem called L2-relaxation is proposed. In contrast to standard formulations, L2-relaxation minimizes the squared Euclidean norm of the weight vector subject to a set of relaxed linear inequality constraints. The magnitude of relaxation, controlled by a tuning parameter, balances the bias and variance. When the variance-covariance (VC) matrix of the individual forecast errors or financial assets exhibits latent group structures -- a block equicorrelation matrix plus a VC for idiosyncratic noises, the solution to L2-relaxation delivers roughly equal within-group weights. Optimality of the new method is established under the asymptotic framework when the number of the cross-sectional units $N$ potentially grows much faster than the time dimension $T$. Excellent finite sample performance of our method is demonstrated in Monte Carlo simulations. Its wide applicability is highlighted in three real data examples concerning empirical applications of microeconomics, macroeconomics, and finance.

Citation extraction

72
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Diebold, F. X. and M. Shin (2019) Machine learning for regularized survey forecast combination: Partially-egalitarian lasso and its derivatives1.00063100%
2Ledoit, O. and M. Wolf (2004) Honey, I shrunk the sample covariance matrix0.92844100%
3DeMiguel, V., L. Garlappi, F. J. Nogales, and R. Uppal (2009) A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms0.92843100%
4Bates, J. M. and C. W. Granger (1969) The combination of forecasts0.8746467%
5Fan, J., Y. Liao, and M. Mincheva (2013) Large covariance estimation by thresholding principal orthogonal complements0.73732100%
6Fan, J., J. Zhang, and K. Yu (2012) Vast portfolio selection with gross-exposure constraints0.73732100%
7Lehrer, S. F. and T. Xie (2017) Box office buzz: does socialmedia data steal the show from model uncertainty when forecasting for hollywood?0.64441100%
8Tibshirani, R (1996) Regression shrinkage and selection via the lasso0.6443267%
9Ledoit, O. and M. Wolf (2020) Analytical nonlinear shrinkage of large-dimensional covariance matrices0.64422100%
10Candes, E. and T. Tao (2007) The Dantzig selector: Statistical estimation when $p$ is much larger than $n$0.64422100%

Showing the top 10 of 72 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Combining Forecasts under Structural Breaks Using Graphical LASSO0.40511
2On LASSO for High Dimensional Predictive Regression0.40511