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
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Diebold, F. X. and M. Shin (2019) Machine learning for regularized survey forecast combination: Partially-egalitarian lasso and its derivatives | 1.000 | 6 | 3 | 100% |
| 2 | Ledoit, O. and M. Wolf (2004) Honey, I shrunk the sample covariance matrix | 0.928 | 4 | 4 | 100% |
| 3 | DeMiguel, V., L. Garlappi, F. J. Nogales, and R. Uppal (2009) A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms | 0.928 | 4 | 3 | 100% |
| 4 | Bates, J. M. and C. W. Granger (1969) The combination of forecasts | 0.874 | 6 | 4 | 67% |
| 5 | Fan, J., Y. Liao, and M. Mincheva (2013) Large covariance estimation by thresholding principal orthogonal complements | 0.737 | 3 | 2 | 100% |
| 6 | Fan, J., J. Zhang, and K. Yu (2012) Vast portfolio selection with gross-exposure constraints | 0.737 | 3 | 2 | 100% |
| 7 | Lehrer, S. F. and T. Xie (2017) Box office buzz: does socialmedia data steal the show from model uncertainty when forecasting for hollywood? | 0.644 | 4 | 1 | 100% |
| 8 | Tibshirani, R (1996) Regression shrinkage and selection via the lasso | 0.644 | 3 | 2 | 67% |
| 9 | Ledoit, O. and M. Wolf (2020) Analytical nonlinear shrinkage of large-dimensional covariance matrices | 0.644 | 2 | 2 | 100% |
| 10 | Candes, E. and T. Tao (2007) The Dantzig selector: Statistical estimation when $p$ is much larger than $n$ | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 72 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Combining Forecasts under Structural Breaks Using Graphical LASSO | 0.405 | 1 | 1 |
| 2 | On LASSO for High Dimensional Predictive Regression | 0.405 | 1 | 1 |