发表机构
Rutgers University; University of Notre Dame（罗格斯大学; 圣母大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对大规模矩阵时间序列，提出对矩阵自回归模型系数矩阵施加降秩约束以进一步降维，并研究估计与秩确定方法，理论和实证表明其统计效率更高。
AI 中文摘要
矩阵时间序列是随时间观测到的矩阵数据序列。在金融、经济学、工程学及许多其他领域的众多应用中，都需要用于此类时间序列的分析工具。为了避免对矩阵进行向量化处理（这会丢失列和行信息）以及传统时间序列分析中的向量自回归框架，\cite{chen2021autoregressive}提出了矩阵自回归（MAR）模型。与对向量化数据采用向量自回归模型相比，该模型保持并利用了矩阵结构，从而实现了显著的维度缩减，并允许明确的解释。然而，当处理大规模矩阵时间序列时，MAR模型仍然面临困难，因为MAR模型中的系数矩阵也很大。在本文中，我们提出通过对MAR模型中的系数矩阵施加降秩约束来实现进一步的维度缩减。研究了估计和秩确定程序。理论研究和实证例子表明，降秩约束可以比MAR模型实现更高的统计效率。
英文摘要
Matrix time series is a series of matrix data observed over time. Analytical tools for such time series is needed in many applications in finance, economics, engineering and many other fields. To avoid the use of vectorization of the matrices which loses the column and row information, and the vector autoregression framework in traditional time series analysis, \cite{chen2021autoregressive} proposed the Matrix Autoregressive (MAR) Model. The model maintains and utilizes the matrix structure, leading to a substantial dimensional reduction and admitting explicit interpretations, comparing with the vector autoregressive model on the vectorized data. However, the MAR model still encounters difficulties in dealing with large dimensional matrix time series as the coefficient matrices in MAR models are also large. In this paper we propose to achieve further dimension reduction through reduced-rank constraints of the coefficient matrices in the MAR model. Estimation and rank determination procedures are studied. Theoretical investigation and empirical examples show that the reduced-rank constraint can achieve higher statistical efficiency than the MAR model.
