Autoregressive models for matrix-valued time series

By Rong Chen, Han Xiao, Dan Yang. Journal of Econometrics, 2018

144 citations recorded by the source corpus.

In finance, economics and many other fields, observations in a matrix form are often generated over time. For example, a set of key economic indicators are regularly reported in different countries every quarter. The observations at each quarter neatly form a matrix and are observed over many consecutive quarters. Dynamic transport networks with observations generated on the edges can be formed as a matrix observed over time. Although it is natural to turn the matrix observations into a long vector, and then use the standard vector time series models for analysis, it is often the case that the columns and rows of the matrix represent different types of structures that are closely interplayed. In this paper we follow the autoregressive structure for modeling time series and propose a novel matrix autoregressive model in a bilinear form that maintains and utilizes the matrix structure to achieve a greater dimensional reduction, as well as more interpretable results. Probabilistic properties of the models are investigated. Estimation procedures with their theoretical properties are presented and demonstrated with simulated and real examples.

Subfields: Economics and Econometrics, Statistics and Probability, Signal Processing

View Paper: https://www.semanticscholar.org/paper/3affc46ed58f30b69dbd7c25080286b186b70f54

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Jinyuan Chang
2. Jianqing Fan
3. Qiwei Yao
4. Lijun Sun
5. Xinyu Chen
6. Lin Yang
7. Jingjing He
8. Elynn Y. Chen

In Statistics and Probability

1. Jinyuan Chang
2. Jianqing Fan
3. Qiwei Yao
4. Elynn Y. Chen
5. Lin Yang
6. Jingjing He
7. Lijun Sun
8. Xinyu Chen

In Signal Processing

1. Qiwei Yao
2. Jianqing Fan
3. Jinyuan Chang
4. Lijun Sun
5. Xinyu Chen
6. Lin Yang
7. Elynn Y. Chen

Citations in the corpus

• Modelling matrix time series via a tensor CP-decomposition (2021, methodology): “The other approaches for modelling matrix time series include: the matrix-coefficient autoregressive models of Chen et al. (2021), and the bilinear transformation segmentation method of Han et al. (2021a).”
• Statistical Inference for High-Dimensional Matrix-Variate Factor Models (2020, background): “∑T s=1 ∥∥∥∥E [ 1 pqCEs EtC]∥∥∥∥2 = Op (1) For interpretation, we again consider the stationary matrix-variate time series (Chen et al., 2018) Et with mean zero and row and column auto-covariance matrices at lag h being UE,h and”
• Bayesian Temporal Factorization for Multidimensional Time Series Prediction (2019, methodology): “Chen et al. [25] extended VAR model for matrix-valued time series data (i.e., a third-order tensor time series) by introducing two AR coefficient matrices to characterize the correlation structure.”