Partial least squares for dependent data

TL;DR

This paper examines the impact of dependence structures on partial least squares algorithms, demonstrating that ignoring dependence can cause inconsistency, and proposes a modified method with improved consistency and predictive power.

Contribution

It introduces a simple modification to PLS for dependent data, ensuring estimator consistency and better performance in real-world applications.

Findings

Ignoring dependence leads to inconsistent estimates.

The modified PLS method achieves consistent estimation.

Real-data example shows improved predictive accuracy.

Abstract

The partial least squares algorithm for dependent data realisations is considered. Consequences of ignoring the dependence for the algorithm performance are studied both theoretically and in simulations. It is shown that ignoring certain non-stationary dependence structures leads to inconsistent estimation. A simple modification of the partial least squares algorithm for dependent data is proposed and consistency of corresponding estimators is shown. A real-data example on protein dynamics llustrates a superior predictive power of the method and the practical relevance of the problem.