Robustness Analysis and Forecasting of High-Dimensional Financial Time Series Data

This paper explores robust forecasting and factor analysis methods for matrix time series data, with a particular focus on datasets characterized by heavy-tailed distributions. It introduces a robust exponential squared loss function to enhance the robustness of estimation methods in the presence of heavy-tailed data. The paper systematically applies the exponential squared loss function to matrix factor models and matrix autoregressive models. Through comprehensive simulations on both non-heavy-tailed and heavy-tailed data, the robustness and effectiveness of the proposed methods are validated. The results show that the proposed Exponentially Penalized Matrix Factor Analysis (EPMFA) method significantly outperforms traditional methods under heavy-tailed conditions, while performing comparably under non-heavy-tailed conditions. Similarly, the Matrix Autoregressive method with exponential squared penalty (EPMRA) demonstrates excellent performance in forecasting under heavy-tailed distributions. This study not only provides robust estimation techniques but also validates their effectiveness in real-world scenarios, offering valuable insights for analyzing heavy-tailed financial matrix time series data.