Regularized Estimation of the Loading Matrix in Factor Models for High-Dimensional Time Series
Xialu Liu, Xin Wang
TL;DR
The paper tackles overparameterization in high-dimensional time series by integrating regularization with dimension reduction through sparse factor models. It develops a regularized estimator that enforces sparsity in the loading matrix within the loading space, improving interpretability and predictive accuracy while relaxing orthogonality and independence assumptions. Theoretical results establish oracle-like convergence and loading-space consistency under mild conditions, and simulations plus a Hawaii tourism application demonstrate superior sparsity recovery and forecasting performance. Overall, the method yields parsimonious, interpretable factor models with competitive predictive power for high-dimensional time series.
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.