A Robust Dynamic Matrix Factor Model for High-Dimensional Time Series with Heavy-Tailed Error Distributions

Abstract

High-dimensional time series analysis has become essential in modern data science, particularly in financial and economic applications where the number of variables often exceeds the available sample size. Classical Vector Autoregressive (VAR) models suffer from parameter explosion in such settings, while standard factor models may fail to capture intrinsic row--column interactions or accommodate non-Gaussian, heavy-tailed noise. This thesis studies a robust dynamic matrix factor model that preserves the matrix structure of the observations to achieve parsimonious dimension reduction, while modeling latent factor dynamics through a Matrix Autoregressive process of order one (MAR(1)).

To address data contamination and heavy-tailed error distributions, the study develops and evaluates robust estimation methodologies, including Robust Matrix Factor Analysis (RMFA) and Iterative Huber Regression (IHR), which employ Huber-type loss functions to down-weight extreme observations. These approaches are contrasted with traditional spectral methods such as $\alpha$-PCA and Projected Estimation. Theoretical results establish consistency and asymptotic normality of the estimators under weaker moment conditions than those required for least-squares-based methods.

Extensive simulation studies demonstrate that while spectral methods perform well under Gaussian noise, robust procedures deliver superior accuracy in loading space recovery and factor-rank determination under heavy-tailed environments. An empirical application to Fama--French $10 \times 10$ portfolio returns identifies a stable $(2,2)$ factor structure, highlighting both the robustness gains and the limitations of linear MAR(1) dynamics under extreme market shocks.