Rank determination in tensor factor model

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