arXiv 14 Dec 2022 · Econometrics · publishedJournal of Econometrics (2024) · 32 citations (OpenAlex)
arXiv:2212.07052 · PDF · DOI · OpenAlex · Extracted main text
This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors are present. The consistency of LASSO is contingent upon two key components: the deviation bound of the cross product of the regressors and the error term, and the restricted eigenvalue of the Gram matrix. We present new probabilistic bounds for these components, suggesting that LASSO's rates of convergence are different from those typically observed in cross-sectional cases. When applied to a mixture of stationary, nonstationary, and cointegrated predictors, LASSO maintains its asymptotic guarantee if predictors are scale-standardized. Leveraging machine learning and macroeconomic domain expertise, LASSO demonstrates strong performance in forecasting the unemployment rate, as evidenced by its application to the FRED-MD database.
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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 | Lee, J. H., Z. Shi, and Z. Gao (2022) On LASSO for predictive regression | 1.000 | 10 | 3 | 100% |
| 2 | Bühlmann, P. and S. van de Geer (2011) Statistics for high-dimensional data: methods, theory and applications | 0.928 | 5 | 4 | 80% |
| 3 | Wainwright, M. J (2019) High-dimensional statistics: A non-asymptotic viewpoint, Volume 48 | 0.928 | 5 | 3 | 80% |
| 4 | Smeekes, S. and E. Wijler (2021) An automated approach towards sparse single-equation cointegration modelling | 0.894 | 7 | 4 | 71% |
| 5 | Wijler, E (2022) A restricted eigenvalue condition for unit-root non-stationary data | 0.874 | 7 | 2 | 100% |
| 6 | Bickel, P. J., Y. Ritov, and A. B. Tsybakov (2009) Simultaneous analysis of Lasso and Dantzig selector | 0.794 | 6 | 3 | 50% |
| 7 | Zhang, R., P. Robinson, and Q. Yao (2019) Identifying cointegration by eigenanalysis | 0.737 | 3 | 3 | 67% |
| 8 | Tibshirani, R (1996) Regression shrinkage and selection via the Lasso | 0.737 | 3 | 2 | 100% |
| 9 | Merlevède, F., M. Peligrad, and E. Rio (2011) A bernstein type inequality and moderate deviations for weakly dependent sequences | 0.644 | 4 | 2 | 50% |
| 10 | Komlós, J., P. Major, and G. Tusnády (1975) An approximation of partial sums of independent rv'-s, and the sample df. i | 0.644 | 2 | 2 | 100% |
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