EconBase
← All papers

Beyond the Oracle Property: Adaptive LASSO in Cointegrating Regressions

Karsten Reichold, Ulrike Schneider

arXiv 8 Oct 2025 · Econometrics

arXiv:2510.07204 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper establishes new asymptotic results for the adaptive LASSO estimator in cointegrating regression models. We study model selection probabilities, estimator consistency, and limiting distributions under both standard and moving-parameter asymptotics. We also derive uniform convergence rates and the fastest local-to-zero rates that can still be detected by the estimator, complementing and extending the results of Lee, Shi, and Gao (2022, Journal of Econometrics, 229, 322--349). Our main findings include that under conservative tuning, the adaptive LASSO estimator is uniformly $T$-consistent and the cut-off rate for local-to-zero coefficients that can be detected by the procedure is $1/T$. Under consistent tuning, however, both rates are slower and depend on the tuning parameter. The theoretical results are complemented by a detailed simulation study showing that the finite-sample distribution of the adaptive LASSO estimator deviates substantially from what is suggested by the oracle property, whereas the limiting distributions derived under moving-parameter asymptotics provide much more accurate approximations. Finally, we show that our results also extend to models with local-to-unit-root regressors and to predictive regressions with unit-root predictors.

Citation extraction

38
references
74
in-text mentions
38
distinct cited
2
self-citations
20,537
main-text words

appendix boundary found by appendix_command · 68% of the source is main text. Read the extracted text to check this.

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., Shi, Z. and Gao, Z (2022) On LASSO for predictive regression1.000145100%
2Mei, Z. and Shi, Z (2024) On lasso for high dimensional predictive regression0.92843100%
3Pötscher, B. M. and Schneider, U (2009) On the distribution of the adaptive LASSO estimator self0.92843100%
4Amann, N. and Schneider, U (2023) Uniform asymptotics and confidence regions based on the adaptive lasso with partially consistent tuning self0.8435360%
5Zou, H (2006) The adaptive Lasso and its oracle properties0.84333100%
6Tu, Y. and Xie, X (2023) Penetrating sporadic return predictability0.73732100%
7Chen, J., Li, D., Li, Y.-N. and Linton, O (2025) Estimating time-varying networks for high-dimensional time series0.64422100%
8Fan, J. and Li, R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties0.64422100%
9Hwang, J. and Valdés, G (2024) Low frequency cointegrating regression with local to unity regressors and unknown form of serial dependence0.64422100%
10Koo, B., Anderson, H. M., Seo, M. H. and Yao, W (2020) High-dimensional predictive regression in the presence of cointegration0.64422100%

Showing the top 10 of 38 scored citations.