High-dimensional predictive regression in the presence of cointegration⇤ Bonsoo Koo Heather Anderson Monash University Monash University Myung Hwan Seo† Wenying Yao Seoul National University Deakin University Abstract 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 co- variates, some of which are highly persistent and potentially cointegrated. We establish the asymptotic properties of the proposed LASSO estimator and validate our theoreti- cal findings using simulation studies. The application of this proposed LASSO approach to forecasting stock returns suggests that a cointegrating relationship among the persis- tent predictors leads to a significant improvement in the prediction of stock returns over various competing forecasting methods with respect to mean squared error. Keywords: Cointegration, High-dimensional predictive regression, LASSO, Return pre- dictability. JEL: C13, C22, G12, G17 ⇤The authors acknowledge financial support from the Australian Research Council Discovery Grant DP150104292. †Corresponding author. His work was supported by Promising-Pioneering ResearcherProgram through Seoul National University(SNU) and from the Ministry of Education of the Republic of Korea and the Na- tional Research Foundation of Korea (NRF-0405-20180026). Author contact details are
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[email protected] 1 1 Introduction Return predictability has been of perennial interest to financial practitioners and scholars within the economics and finance professions since the early work of Dow (1920). To this end, empirical studies employ linear predictive regression models, as illustrated by Stam- baugh (1999), Binsbergen et al.