Explanatory variables in a predictive regression typically exhibit low signal strength and various degrees of persistence. Variable selection in such a context is of great importance. In this paper, we explore the pitfalls and possibilities of the LASSO methods in this predictive regression framework. In the presence of stationary, local unit root, and cointegrated predictors, we show that the adaptive LASSO cannot asymptotically eliminate all cointegrating variables with zero regression coefficients. This new finding motivates a novel post-selection adaptive LASSO, which we call the twin adaptive LASSO (TAlasso), to restore variable selection consistency. Accommodating the system of heterogeneous regressors, TAlasso achieves the well-known oracle property. In contrast, conventional LASSO fails to attain coefficient estimation consistency and variable screening in all components simultaneously. We apply these LASSO methods to evaluate the short- and long-horizon predictability of S&P 500 excess returns.

预测回归中的解释变量通常表现出低信号强度和不同程度的持续性。在这种情况下，变量选择非常重要。在本文中，我们探讨了 LASSO 方法在这个预测回归框架中的缺陷和可能性。在存在平稳、局部单位根和协整预测变量的情况下，我们表明自适应 LASSO 不能渐近消除所有回归系数为零的协整变量。这一新发现激发了一种新的选择后自适应 LASSO，我们称之为双自适应 LASSO(TAlasso)，恢复变量选择的一致性。适应异构回归器系统，TAlasso 实现了众所周知的预言属性。相比之下，传统的 LASSO 无法同时在所有组件中获得系数估计一致性和变量筛选。我们应用这些 LASSO 方法来评估标准普尔 500 超额收益的短期和长期可预测性。