Problem
Research questions and friction points this paper is trying to address.
Matrix time series
Matrix autoregressive model
Dimension reduction
Reduced-rank constraints
Reduced-Rank Autoregressive Models for Matrix Time Series
🤖 AI Summary
This study addresses the computational challenges arising from the explosive growth in coefficient matrix dimensions when applying matrix autoregressive (MAR) models to high-dimensional time series. To this end, we propose a reduced-rank MAR model that imposes additional dimensionality reduction on the coefficient matrices while preserving the inherent matrix structure of the data. This approach effectively reduces parameter space complexity and enhances statistical efficiency. We systematically develop the corresponding parameter estimation and rank determination procedures. Both theoretical analysis and empirical studies demonstrate that the proposed method achieves significantly superior statistical efficiency compared to conventional MAR models, providing an effective new paradigm for modeling high-dimensional matrix-valued time series.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Matrix Time Series
Reduced-Rank Constraints
Matrix Autoregressive Model
Dimension Reduction
Statistical Efficiency
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