We show that the activation knot of a potentially non-stationary regressor on the adaptive Lasso solution path in autoregressions can be leveraged for selection-free inference about a unit root. The resulting test has asymptotic power against local alternatives in $1/T$ neighbourhoods, unlike post-selection inference methods based on consistent model selection. Exploiting the information enrichment principle devised by Reinschl\"ussel and Arnold arXiv:2402.16580 [stat.ME] to improve the Lasso-based selection of ADF models, we propose a composite statistic and analyse its asymptotic distribution and local power function. Monte Carlo evidence shows that the combined test dominates the comparable post-selection inference methods of Tibshirani et al. [JASA, 2016, 514, 600-620] and may surpass the power of established unit root tests against local alternatives. We apply the new tests to groundwater level time series for Germany and find evidence rejecting stochastic trends to explain observed long-term declines in mean water levels.

翻译：本文证明，在自回归模型中，利用自适应Lasso解路径上潜在非平稳回归量的激活节点，可实现无需模型选择的单位根推断。与基于一致性模型选择的后选择推断方法不同，所得检验对$1/T$邻域内的局部备择假设具有渐近功效。借鉴Reinschlüssel与Arnold在arXiv:2402.16580 [stat.ME]中提出的信息富集原理以改进基于Lasso的ADF模型选择，我们构建了一个复合统计量，并分析了其渐近分布与局部功效函数。蒙特卡洛模拟表明，该复合检验优于Tibshirani等人[JASA, 2016, 514, 600-620]提出的后选择推断方法，且在局部备择假设下可能超越传统单位根检验的效力。我们将新检验应用于德国地下水位时间序列，发现拒绝用随机趋势解释观测到的水位长期下降趋势的证据。