Factor Models for High-Dimensional Tensor Time Series

Abstract

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 article we present a factor model approach to the analysis of high-dimensional dynamic tensor time series and multi-category dynamic transport networks. This article presents two estimation procedures along with their theoretical properties and simulation results. We present two applications to illustrate the model and its interpretations.

KEYWORDS:

• Autocovariance matrices
• Cross-covariance matrices
• Dimension reduction
• Dynamic transport network
• Eigen-analysis
• Factor models
• Import–export
• Tensor time series
• Traffic
• Unfolding

Funding

Division of Computing and Communication Foundations; Division of Information and Intelligent Systems;Hong Kong CRF;Division of Mathematical Sciences;Division of Mathematical Sciences;

Additional information

Funding

Chen’s research is supported in part by National Science Foundation grants DMS-1503409, DMS-1737857, IIS-1741390, CCF-1934924 and DMS-2027855. Yang’s research is supported in part by NSF grant IIS-1741390, Hong Kong GRF 17301620 and CRF C7162-20GF. Zhang’s research is supported in part by NSF grants DMS-1721495, IIS-1741390 and CCF-1934924. The authors thank the editor, an associate editor, and three anonymous referees for their helpful comments.