Recent Advances in Dynamic Shrinkage in High-Dimensional Regression Models

Accepted April 2026

Abstract

This survey reviews recent advances in dynamic shrinkage models for time-varying parameter estimation and variable selection, with applications in high-dimensional time series analysis. We begin by introducing foundational static shrinkage approaches including Ridge, Lasso, Elastic-Net, Bayesian Lasso, Horseshoe and Spike-and-Slab priors. Building on this foundation, we focus on dynamic extensions that allow the shrinkage mechanism to evolve over time, enabling models to adapt to structural breaks and regime changes. We discuss Bayesian and frequentist formulations, computational strategies, and empirical performance in modern econometric applications.