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 the LASSO methods in this predictive regression framework with mixed degrees of persistence. With the presence of stationary, unit root and cointegrated predictors, we show that the adaptive LASSO maintains the consistent variable selection and the oracle property due to its penalty scheme that accommodates the system of regressors . On the contrary, conventional LASSO does not have this desirable feature as the penalty is imposed according to the marginal behavior of each individual regressor  . We demonstrate this theoretical property via extensive Monte Carlo simulations , and evaluate its empirical performance for short- and long-horizon stock return predictability  .
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 .
D
the
R
With
In
R
maintains the consistent variable selection and the oracle property due to its penalty scheme that
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
R
regressors
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
R
does not have this desirable feature as the
fails to attain coefficient estimation consistency and variable screening in all components simultaneously, since its
A
only
R
this theoretical property
the theoretical properties
R
, and evaluate its empirical performance for
. These LASSO-type methods are applied to evaluate
R
stock return predictability
predictability of S
A
P 500 excess return