Rank determination in tensor factor model

Yuefeng Han, Rong Chen, Cun Hui Zhang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Factor model is an appealing and effective analytic tool for high-dimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of factors for tensor factor models where the signal part of an observed tensor time series assumes a Tucker decomposition with the core tensor as the factor tensor. The task is to determine the dimensions of the core tensor. One of the proposed criteria is similar to information based criteria of model selection, and the other is an extension of the approaches based on the ratios of consecutive eigenvalues often used in factor analysis for panel time series. Theoretically results, including sufficient conditions and convergence rates, are established. The results include the vector factor models as special cases, with an additional convergence rates. Simulation studies provide promising finite sample performance for the two criteria.

Original languageEnglish (US)
Pages (from-to)1726-1803
Number of pages78
JournalElectronic Journal of Statistics
Issue number1
StatePublished - 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • High-dimensional tensor data
  • Tucker decomposition
  • eigenvalues
  • factor model
  • rank determination


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