A PLS-Integrated LASSO Method with Application in Index Tracking

TL;DR

This paper introduces a novel PLS-integrated Lasso (PLS-Lasso) method that combines dimension reduction and regression, with two formulations and algorithms, demonstrating promising results in financial index tracking.

Contribution

The paper presents the first integration of PLS with Lasso regression, providing two formulations and algorithms with convergence guarantees for improved index tracking.

Findings

PLS-Lasso outperforms traditional Lasso in index tracking tasks.

Two formulations, PLS-Lasso-v1 and v2, show effective convergence.

Promising results demonstrate the method's potential in financial applications.

Abstract

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.