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On LASSO for High Dimensional Predictive Regression

Ziwei Mei, Zhentao Shi

arXiv 14 Dec 2022 · Econometrics · publishedJournal of Econometrics (2024) · 32 citations (OpenAlex)

arXiv:2212.07052 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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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
1Lee, J. H., Z. Shi, and Z. Gao (2022) On LASSO for predictive regression1.000103100%
2Bühlmann, P. and S. van de Geer (2011) Statistics for high-dimensional data: methods, theory and applications0.9285480%
3Wainwright, M. J (2019) High-dimensional statistics: A non-asymptotic viewpoint, Volume 480.9285380%
4Smeekes, S. and E. Wijler (2021) An automated approach towards sparse single-equation cointegration modelling0.8947471%
5Wijler, E (2022) A restricted eigenvalue condition for unit-root non-stationary data0.87472100%
6Bickel, P. J., Y. Ritov, and A. B. Tsybakov (2009) Simultaneous analysis of Lasso and Dantzig selector0.7946350%
7Zhang, R., P. Robinson, and Q. Yao (2019) Identifying cointegration by eigenanalysis0.7373367%
8Tibshirani, R (1996) Regression shrinkage and selection via the Lasso0.73732100%
9Merlevède, F., M. Peligrad, and E. Rio (2011) A bernstein type inequality and moderate deviations for weakly dependent sequences0.6444250%
10Komlós, J., P. Major, and G. Tusnády (1975) An approximation of partial sums of independent rv'-s, and the sample df. i0.64422100%

Showing the top 10 of 60 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
1Beyond the Oracle Property: Adaptive LASSO in Cointegrating Regressions with Local-to-Unity Regressors0.92843
2LASSO Inference for High Dimensional Predictive Regressions0.73733
3Inference in Non-stationary High-Dimensional VARs0.58531
42512.020920.51121
5A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates0.40511
6Nickell Meets Stambaugh: A Tale of Two Biases in Panel Predictive Regressions0.40511