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.
Han’s research is supported in part by National Science Foundation grant IIS-1741390. Zhang’s research is supported in part by NSF grants DMS-1721495, IIS-1741390, CCF-1934924 and DMS-2052949 Chen’s research is supported in part by National Science Foundation grants DMS-1503409, DMS-1737857, IIS-1741390 and DMS-2052949
"Rank determination in tensor factor model." Electron. J. Statist. 16 (1) 1726 - 1803, 2022. https://doi.org/10.1214/22-EJS1991