High-dimensional predictive regression in the presence of cointegration

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 a cointegrating relationship among the persistent predictors leads to a significant improvement in the prediction of stock returns over various competing forecasting methods with respect to mean squared error.