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On LASSO for Predictive Regression

Ji Hyung Lee, Zhentao Shi and Zhan Gao

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Abstract: 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.

New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2018-10, Revised 2018-10
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