Autoregressive models for matrix-valued time series

In finance, economics and many other fields, observations in a matrix form are often generated over time. For example, set of key economic indicators regularly reported different countries every quarter. The at each quarter neatly observed consecutive quarters. Dynamic transport networks with on the edges can be formed as Although it is natural to turn into long vectors, then use standard vector time series 2 models for analysis, case that columns rows represent types structures closely interplayed. this paper we follow autoregression modeling propose novel autoregressive model bilinear maintains utilizes structure achieve substantial dimensional reduction, well more interpretability. Probabilistic properties investigated. Estimation procedures their theoretical presented demonstrated simulated real examples.