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：我们证明，在自回归模型中，自适应Lasso解路径上潜在非平稳回归变量的激活结可用于实现无需选择的单位根推断。与基于一致模型选择的选择后推断方法不同，所得检验对$1/T$邻域内的局部备择具有渐近功效。利用Reinschlüssel和Arnold（arXiv:2402.16580 [stat.ME]）提出的信息富集原理改进基于Lasso的ADF模型选择，我们提出一种复合统计量，并分析其渐近分布与局部功效函数。蒙特卡洛证据表明，该组合检验优于Tibshirani等（JASA, 2016, 514, 600-620）的可比选择后推断方法，且可能超越经典单位根检验对局部备择的功效。我们将新检验应用于德国地下水位时间序列，发现证据拒绝随机趋势假说，从而解释观测到的平均水位长期下降现象。