Cointegrated Regressors: Where Folded Concave Penalties Go Beyond LASSO

研究问题: 在高维预测回归中，当回归变量之间存在协整关系时，LASSO 的凸惩罚会过度压缩协整变量系数、无法给出一致参数估计，摘要据此提出应如何改进正则化方法。
方法与思路: 作者采用折叠凹惩罚（FCP），包括 SCAD 与 MCP，替代 LASSO 的凸惩罚，并建立两个渐近结果：惩罚回归的局部 oracle 性质，以及带惩罚水平约束的回归的全局 oracle 性质。
材料陈述的贡献: 摘要称，带惩罚水平约束的全局 oracle 性质保证全局解一致估计真实系数并具有 oracle 预测表现；模拟研究与欧元区失业率预测应用显示，FCP 相对 LASSO 改善了变量选择与样本外预测。
阅读关注点: 应核对协整设定与识别假设的具体表述、两个 oracle 结果的成立条件与惩罚水平约束如何选取，以及模拟设计和欧元区失业率数据、评价指标能否支持摘要所述改进。
阅读边界: 仅依据摘要，无法判断定理假设是否合理、证明是否完整、模拟与实证细节及结果稳健性；摘要未说明惩罚参数选择、样本规模与对比方法的具体设置。

DeepSeek Flash · 2026-10-14

原文摘要

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.

摘要来源：arXiv

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