High-Dimensional Predictive Regression in the Presence of Cointegration

Abstract

While a great number of predictive variables for stock returns have been suggested, their prediction power is unstable. We propose a Least Absolute Shrinkage and Selection Operator (LASSO) estimator of a predictive regression in which stock returns are conditioned on a large set of lagged covariates, some of which are highly persistent and potentially cointegrated. We establish the asymptotic properties of the proposed LASSO estimator and validate our theoretical findings using simulation studies. The application of this proposed LASSO approach to forecasting stock returns suggests that cointegrating relationships among the persistent predictors leads to a significant improvement in the prediction of stock returns over various competing models in the mean squared error sense.