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Cointegrated Regressors: Where Folded Concave Penalties Go Beyond LASSO

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

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.

Suggested Citation

  • Hongqi Chen & Chengwang Liao & Ziwei Mei & Zhentao Shi, 2026. "Cointegrated Regressors: Where Folded Concave Penalties Go Beyond LASSO," Papers 2610.14617, arXiv.org, revised Oct 2026.
    • Handle: RePEc:arx:papers:2610.14617
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    File URL: https://arxiv.org/pdf/2610.14617
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