Regularized Estimation of the Loading Matrix in Factor Models for High-Dimensional Time Series

TL;DR

This paper proposes a regularized estimation method for the loading matrix in high-dimensional factor models, combining sparsity and interpretability to improve analysis of complex time series data.

Contribution

It introduces a novel regularized estimator with a penalty term for sparse loading matrices, enhancing interpretability and reducing parameters in high-dimensional factor models.

Findings

Estimator performs well in simulations

Method improves interpretability of factors

Applied successfully to Hawaii tourism data

Abstract

High-dimensional data analysis using traditional models suffers from overparameterization. Two types of techniques are commonly used to reduce the number of parameters - regularization and dimension reduction. In this project, we combine them by imposing a sparse factor structure and propose a regularized estimator to further reduce the number of parameters in factor models. A challenge limiting the widespread application of factor models is that factors are hard to interpret, as both factors and the loading matrix are unobserved. To address this, we introduce a penalty term when estimating the loading matrix for a sparse estimate. As a result, each factor only drives a smaller subset of time series that exhibit the strongest correlation, improving the factor interpretability. The theoretical properties of the proposed estimator are investigated. The simulation results are presented to confirm that our algorithm performs well. We apply our method to Hawaii tourism data.