LASSO Estimation of Structural Break Models via Cross‐Validation

This article develops a novel approach to consistently identify the number of break points in structural break models. We first propose a group LASSO procedure combined with a block segmentation scheme to quickly identify an overestimated set of possible break points. This serves as a rough ‘screening’ step and is therefore less sensitive to the choice of the tuning parameter. Second, we perform a refining step to extract the best subset from these candidate break points based on a pre‐specified information criterion, whose performance depends heavily on the penalty magnitude. To overcome this limitation, we develop a sophisticated cross‐validation criterion coupled with an order‐preserved sample‐splitting strategy to consistently determine the number of breaks. Numerical examples show that our approach outperforms existing works in terms of estimation accuracy and computational efficiency. Finally, our method is illustrated via analyzing the nonlinear effects of 401(k) retirement programs on savings.