# Factor Models for Matrix-Valued High-Dimensional Time Series

arXiv: https://arxiv.org/abs/1610.01889 · HTML: https://mlsanity.com/paper/1610.01889/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2016.

## Built on by (most cited first, 9 of 9)

- [Modelling matrix time series via a tensor CP-decomposition](https://mlsanity.com/paper/2112.15423/) (2021)
- [Tucker Diffusion Model for High-dimensional Tensor Generation](https://mlsanity.com/paper/2604.00481/) (2026)
- [Regression for matrix-valued data via Kronecker products factorization](https://mlsanity.com/paper/2404.19220/) (2024)
- [Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges](https://mlsanity.com/paper/2405.18412/) (2024)
- [TEAFormers: TEnsor-Augmented Transformers for Multi-Dimensional Time Series Forecasting](https://mlsanity.com/paper/2410.20439/) (2024)
- [Mining the Factor Zoo: Estimation of Latent Factor Models with Sufficient Proxies](https://mlsanity.com/paper/2212.12845/) (2022)
- [Robust bilinear factor analysis based on the matrix-variate t distribution](https://mlsanity.com/paper/2401.02203/) (2024)
- [Sparsity-Induced Global Matrix Autoregressive Model with Auxiliary Network Data](https://mlsanity.com/paper/2503.08579/) (2025)
- [Feature Augmentations for High-Dimensional Learning](https://mlsanity.com/paper/2509.00232/) (2025)

## Abstract (arXiv)

In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many companies are reported over time. Although it is natural to turn a matrix observation into a long vector then use standard vector time series models or factor analysis, it is often the case that the columns and rows of a matrix represent different sets of information that are closely interrelated in a very structural way. We propose a novel factor model that maintains and utilizes the matrix structure to achieve greater dimensional reduction as well as finding clearer and more interpretable factor structures. Estimation procedure and its theoretical properties are investigated and demonstrated with simulated and real examples.