|
Abstract:
|
Matrix time series, a sequence of observations in matrix form, are often observed in finance, economics and many other fields. For example, key economic indicators are regularly reported in different countries every quarter. Such observations 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. To avoid the use of vectorization of the matrices that losses the column and row structure information, the Matrix Autoregressive Models of Chen et al (2019) uses a bilinear form in an autoregressive model that maintains and utilizes the matrix structure to achieve a substantial dimensional reduction, as well as more interpretability. However, the model still encounters difficulties in dealing with high dimensional matrix time series. In this paper we propose to achieve further dimension reduction through a reduced rank representation of the coefficient matrices in the matrix AR model. Probabilistic properties of the model are investigated. Estimation procedures with their theoretical properties are presented and demonstrated with simulated and real examples.
|
