Structural breaks detection and variable selection in dynamic linear regression via the Iterative Fused LASSO in high dimension

TL;DR

This paper introduces an efficient iterative Fused LASSO-based method for simultaneous variable selection and structural break detection in high-dimensional linear regression models, validated through simulations and real-world data.

Contribution

It develops a novel algorithm that effectively handles high-dimensional data for variable selection and structural break detection, outperforming existing methods.

Findings

Algorithm performs well in high-dimensional settings

Validated through simulations and real-world case studies

Demonstrates robustness and practical utility

Abstract

We aim to develop a time series modeling methodology tailored to high-dimensional environments, addressing two critical challenges: variable selection from a large pool of candidates, and the detection of structural break points, where the model's parameters shift. This effort centers on formulating a least squares estimation problem with regularization constraints, drawing on techniques such as Fused LASSO and AdaLASSO, which are well-established in machine learning. Our primary achievement is the creation of an efficient algorithm capable of handling high-dimensional cases within practical time limits. By addressing these pivotal challenges, our methodology holds the potential for widespread adoption. To validate its effectiveness, we detail the iterative algorithm and benchmark its performance against the widely recognized Path Algorithm for Generalized Lasso. Comprehensive simulations and performance analyses highlight the algorithm's strengths. Additionally, we demonstrate the methodology's applicability and robustness through simulated case studies and a real-world example involving a stock portfolio dataset. These examples underscore the methodology's practical utility and potential impact across diverse high-dimensional settings.