Factor Models for High-Dimensional Tensor Time Series

Abstract

Large tensor (multi-dimensional array) data are now routinely collected 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 for analyzing high-dimensional dynamic tensor time series and multi-category dynamic transport networks. Two estimation procedures along with their theoretical properties and simulation results are presented. Two applications are used to illustrate the model and its interpretations.

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• Multi-linear Tensor Autoregressive Models
• Testing and Support Recovery of Correlation Structures for Matrix-Valued Observations with an Application to Stock Market Data