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Cointegrated Regressors: Where Folded Concave Penalties Go Beyond LASSO

  • Hongqi Chen
  • Chengwang Liao
  • Ziwei Mei
  • Zhentao Shi
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Abstract

LASSO is one of the most popular regularization methods for high-dimensional regression models. While cointegration is common in practical applications of predictive regressions with many regressors, the convex penalty of LASSO overly suppresses the coefficients of cointegrated regressors and therefore fails to deliver consistent parameter estimation. We employ folded concave penalties (FCP), including the well-known SCAD and MCP, to address this issue. Using FCP, we establish two asymptotic results: (i) a local oracle property for the penalized regression, and (ii) a global oracle property for regressions with a penalty-level constraint. In particular, the latter guarantees a global solution that consistently estimates the true coefficients and enjoys oracle prediction performance. Simulation studies and an application to predicting the euro area unemployment rate show that FCP improves variable selection and out-of-sample prediction relative to LASSO.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026cointegrated,
  title = {{Cointegrated Regressors: Where Folded Concave Penalties Go Beyond LASSO}},
  author = {Hongqi Chen and Chengwang Liao and Ziwei Mei and Zhentao Shi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14617},
  eprint = {2610.14617},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14617},
}
RIS
TY  - UNPB
TI  - Cointegrated Regressors: Where Folded Concave Penalties Go Beyond LASSO
AU  - Hongqi Chen
AU  - Chengwang Liao
AU  - Ziwei Mei
AU  - Zhentao Shi
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.14617
UR  - https://arxiv.org/abs/2610.14617
AB  - LASSO is one of the most popular regularization methods for high-dimensional regression models. While cointegration is common in practical applications of predictive regressions with many regressors, the convex penalty of LASSO overly suppresses the coefficients of cointegrated regressors and therefore fails to deliver consistent parameter estimation. We employ folded concave penalties (FCP), including the well-known SCAD and MCP, to address this issue. Using FCP, we establish two asymptotic results: (i) a local oracle property for the penalized regression, and (ii) a global oracle property for regressions with a penalty-level constraint. In particular, the latter guarantees a global solution that consistently estimates the true coefficients and enjoys oracle prediction performance. Simulation studies and an application to predicting the euro area unemployment rate show that FCP improves variable selection and out-of-sample prediction relative to LASSO.
ER  -