團隊

Large tensor (multi-dimensional array) data routinely appear nowadays in a wide range of applications, due to modern data collection capabilities. Often such observations are taken over time, forming tensor time series. In this paper we present a factor model approach to the analysis of high-dimensional dynamic tensor time series and multi-category dynamic transport networks. Two estimation procedures are presented along with their theoretical properties and simulation results. Two applications are used to illustrate the model and its interpretations.

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.