A0452
Title: Envelope matrix autoregressive models
Authors: S Yaser Samadi - Southern Illinois University Carbondale (United States)
Tharindu De Alwis - University of West Florida (United States) [presenting]
Abstract: Matrix-valued data, common in many scientific fields, presents challenges for traditional time series analysis due to overparametrization and the loss of structural information when using vectorization. The matrix autoregressive (MAR) model was developed to overcome these limitations by preserving the original matrix structure, thus reducing dimensions and allowing for clearer data interpretations. However, high-dimensional matrix time series still pose a problem for MAR models because of the large coefficient matrices, making it difficult to discern relevant information. To address this, envelope-based MAR (EMAR) models are proposed. The EMAR approach significantly enhances efficiency in estimation and forecasting by reducing parameters and establishing a connection between the mean function and covariance structure. This is achieved through the use of minimal reducing subspaces of covariance matrices. The asymptotic properties of the estimators are established, and simulation studies (under both normal and non-normal conditions) are conducted to compare their efficiency and accuracy against existing methods. Additionally, the practical effectiveness of the EMAR approach is demonstrated with two real-world applications in economics and business.
