A PLS-Integrated LASSO Method with Application in Index Tracking
This is an incremental improvement for researchers and practitioners in multivariate data analysis, particularly in finance.
The paper tackles the problem of separating dimension reduction from regression in multivariate analysis by introducing PLS-Lasso, which integrates these steps; it shows promising results in financial index tracking compared to Lasso.
In traditional multivariate data analysis, dimension reduction and regression have been treated as distinct endeavors. Established techniques such as principal component regression (PCR) and partial least squares (PLS) regression traditionally compute latent components as intermediary steps -- although with different underlying criteria -- before proceeding with the regression analysis. In this paper, we introduce an innovative regression methodology named PLS-integrated Lasso (PLS-Lasso) that integrates the concept of dimension reduction directly into the regression process. We present two distinct formulations for PLS-Lasso, denoted as PLS-Lasso-v1 and PLS-Lasso-v2, along with clear and effective algorithms that ensure convergence to global optima. PLS-Lasso-v1 and PLS-Lasso-v2 are compared with Lasso on the task of financial index tracking and show promising results.