This paper derives new asymptotic results for the adaptive LASSO estimator in cointegrating regressions, allowing for uncertainty about whether the regressors are exact unit root processes. We study model selection probabilities, estimator consistency, and limiting distributions under standard and moving-parameter asymptotics. We further derive uniform convergence rates and the fastest local-to-zero rates detectable by the estimator under conservative and consistent tuning. For consistent tuning, we construct confidence regions that are easy to implement, uniformly valid over the parameter space, and achieve sure asymptotic coverage without requiring knowledge or estimation of local-to-unity or long-run covariance parameters. Simulation results reveal that the finite-sample distribution of the adaptive LASSO estimator can deviate substantially from the oracle property, whereas moving-parameter asymptotics provide much more accurate approximations. Consequently, in addition to being infeasible in applications due to their dependence on non-estimable nuisance parameters, oracle-based confidence regions are often too small to achieve adequate coverage in empirically relevant scenarios with small but non-zero coefficients. In contrast, the proposed confidence regions are always feasible and deliver reliable coverage across the parameter space. An empirical application to predicting the U.S. unemployment rate illustrates their practical usefulness for quantifying uncertainty around adaptive LASSO estimates.

翻译：本文推导了协整回归中自适应LASSO估计量的新渐近性质，允许回归变量是否为精确单位根过程存在不确定性。我们研究了标准渐近与移动参数渐近框架下的模型选择概率、估计量相合性及极限分布。进一步推导了一致收敛速率，以及在保守调参与相合调参下估计量可检测的最快局部趋零速率。针对相合调参情形，我们构建了易于实现的置信区域，这些区域在参数空间上具有一致有效性，且无需获知或估计局部趋近单位根参数与长期协方差参数即可确保渐近覆盖。模拟结果表明：自适应LASSO估计量的有限样本分布可能显著偏离Oracle性质，而移动参数渐近则能提供更为精确的近似。因此，基于Oracle性质的置信区域不仅因依赖不可估计的冗余参数而在实际应用中不可行，且在系数较小非零的经验相关场景中往往因区间过窄而无法达到充分覆盖。相比之下，本文提出的置信区域始终具有可行性，并在整个参数空间内提供可靠的覆盖效果。通过对美国失业率预测的实证应用，展示了该方法在量化自适应LASSO估计不确定性方面的实用价值。