Rank Determination in Tensor Factor Model

TL;DR

This paper introduces two new criteria for accurately determining the number of factors in tensor factor models, with theoretical guarantees and promising simulation results.

Contribution

It develops novel criteria for tensor factor model order determination, extending existing methods and providing theoretical analysis and practical validation.

Findings

Two criteria effectively determine tensor factor model dimensions.

Theoretical results include convergence rates and conditions.

Simulation studies show good finite sample performance.

Abstract

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.