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：我们提出了一种新方法，用于在基于自适应Lasso的自回归模型一致且具备Oracle效率的估计中，对潜在非平稳回归变量的权重进行赋值。这一增强权重基于一种统计量，该统计量利用了时间序列回归中OLS估计量在不同积分阶数下概率收敛速度的显著差异。我们提供了理论结果，证明当基于调优准则选择ℓ1惩罚参数时，所提方法在检测平稳性方面的优势。蒙特卡洛实验表明，与Kock [Econom. Theory, 32, 2016, 243-259]所建议的基于OLS的权重相比，我们的方法具有更优性能。我们将改进后的估计方法应用于欧元引入后德国通胀率的模型选择。结果表明，能源大宗商品价格通胀率与整体通胀率最适宜用平稳自回归模型描述。