We propose a novel approach to elicit the weight of a potentially non-stationary regressor in the consistent and oracle-efficient estimation of autoregressive models using the adaptive Lasso. The enhanced weight builds on a statistic that exploits distinct orders in probability of the OLS estimator in time series regressions when the degree of integration differs. We provide theoretical results on the benefit of our approach for detecting stationarity when a tuning criterion selects the $\ell_1$ penalty parameter. Monte Carlo evidence shows that our proposal is superior to using OLS-based weights, as suggested by Kock [Econom. Theory, 32, 2016, 243-259]. We apply the modified estimator to model selection for German inflation rates after the introduction of the Euro. The results indicate that energy commodity price inflation and headline inflation are best described by stationary autoregressions.

翻译：本文提出了一种新颖方法，在利用自适应Lasso进行自回归模型的一致且oracle有效估计时，用于提取潜在非平稳回归量的权重。该增强权重基于一个统计量构建，该统计量利用了时间序列回归中当积分阶数不同时OLS估计量的不同概率阶数。我们提供了理论结果，证明当调优准则选择$\ell_1$惩罚参数时，我们的方法在检测平稳性方面的优势。蒙特卡洛模拟证据表明，我们的方案优于使用基于OLS的权重（如Kock [Econom. Theory, 32, 2016, 243-259]所建议）。我们将改进的估计量应用于欧元引入后德国通货膨胀率的模型选择。结果表明，能源商品价格通胀和总体通胀最适合用平稳自回归模型描述。