Reduced rank matrix autoregression and its application

In the case of high dimensions or high row (column) variable correlation, the existing matrix autoregression will face dual challenges of declining prediction accuracy and insufficient interpretation. In order to solve the above problems, this paper proposes reduced rank matrix autoregression and reduced rank iterative least squares method. By setting the low-rank structure of coefficient matrix, reducing dimensionality of independent variables and parameters to be estimated, this model can not only ensure estimation accuracy and increase prediction accuracy, but also simplify relationship between variables and improve interpretation ability. Moreover, this paper proves the theoretical asymptotic properties, and highlights that the minimum eigenvalue ratio criterion can be used to determine the model rank. Numerical simulations show that the model and estimation method outperform under the rank constraint. Finally, the proposed model is applied to urban air quality research, which fully depicts the advantages of dimensionality reduction, denoising, accurate prediction and effective interpretation. © 2023 Systems Engineering Society of China. All rights reserved.