# Rank Determination in Tensor Factor Model

arXiv: https://arxiv.org/abs/2011.07131 · HTML: https://mlsanity.com/paper/2011.07131/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2020.

## Built on by (most cited first, 8 of 8)

- [Tensor Principal Component Analysis in High Dimensional CP Models](https://mlsanity.com/paper/2108.04428/) (2021)
- [Factor Augmented Tensor-on-Tensor Neural Networks](https://mlsanity.com/paper/2405.19610/) (2024)
- [Multi-dimensional domain generalization with low-rank structures](https://mlsanity.com/paper/2309.09555/) (2023)
- [Econometrics of Machine Learning Methods in Economic Forecasting](https://mlsanity.com/paper/2308.10993/) (2023)
- [TEAFormers: TEnsor-Augmented Transformers for Multi-Dimensional Time Series Forecasting](https://mlsanity.com/paper/2410.20439/) (2024)
- [Supervised Dynamic Dimension Reduction with Deep Neural Network](https://mlsanity.com/paper/2508.03546/) (2025)
- [Tensor PCA from basis in tensor space](https://mlsanity.com/paper/2305.02803/) (2023)
- [Decomposition of linear tensor transformations](https://mlsanity.com/paper/2309.07819/) (2023)

## Abstract (arXiv)

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.