Autoregressive models for matrix-valued time series

Rong Chen, Han Xiao, Dan Yang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 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 long vectors, then use the standard vector time series 2 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 autoregression 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 substantial dimensional reduction, as well as more interpretability. Probabilistic properties of the models are investigated. Estimation procedures with their theoretical properties are presented and demonstrated with simulated and real examples.

Original languageEnglish (US)
Pages (from-to)539-560
Number of pages22
JournalJournal of Econometrics
Issue number1
StatePublished - May 2021

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • Autoregressive
  • Bilinear
  • Economic indicators
  • Kronecker product
  • Matrix-valued time series
  • Multivariate time series
  • Nearest Kronecker product projection
  • Prediction


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