A typical predictive regression employs a multitude of potential regressors with various degrees of persistence while their signal strength in explaining the dependent variable is often low . Variable selection in such  context is of great importance. In this paper, we explore the pitfalls and possibilities of  LASSO methods in this predictive regression framework with mixed degrees of persistence . In the presence of stationary, unit root and cointegrated predictors, we show that the adaptive LASSO asymptotically breaks cointegrated groups although it cannot wipe out all inactive cointegrating variables . This new finding motivates a simple but novel post-selection adaptive LASSO, which we call the twin adaptive LASSO (TAlasso), to fix variable selection inconsistency. TAlasso's penalty scheme accommodates the system of heterogeneous regressors, and it recovers the well-known oracle property that implies variable selection consistency and optimal rate of convergence for all three types of regressors. On the contrary , conventional LASSO fails to attain coefficient estimation consistency and variable screening in all components simultaneously , since its penalty is imposed according to the marginal behavior of each individual regressor only. We demonstrate the theoretical properties via extensive Monte Carlo simulations. These LASSO-type methods are applied to evaluate short- and long-horizon predictability of S  P 500 excess return .
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 .
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while their signal strength in explaining the dependent variable is often low
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with mixed degrees of persistence
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asymptotically breaks cointegrated groups although it cannot wipe out all inactive cointegrating variables
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fix variable selection inconsistency. TAlasso's penalty scheme accommodates
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that implies variable selection consistency and optimal rate of convergence for all three types of regressors. On the contrary
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