# Time-Varying Matrix Factor Models

arXiv: https://arxiv.org/abs/2404.01546 · HTML: https://mlsanity.com/paper/2404.01546/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2024.

## Built on by (most cited first, 3 of 3)

- [Tensor-Fused Multi-View Graph Contrastive Learning](https://mlsanity.com/paper/2410.15247/) (2024)
- [TEAFormers: TEnsor-Augmented Transformers for Multi-Dimensional Time Series Forecasting](https://mlsanity.com/paper/2410.20439/) (2024)
- [Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection](https://mlsanity.com/paper/2605.19122/) (2026)

## Abstract (arXiv)

Matrix-variate data of high dimensions are frequently observed in finance and economics, spanning extended time periods, such as the long-term data on international trade flows among numerous countries. To address potential structural shifts and explore the matrix structure's informational context, we propose a time-varying matrix factor model. This model accommodates changing factor loadings over time, revealing the underlying dynamic structure through nonparametric principal component analysis and facilitating dimension reduction. We establish the consistency and asymptotic normality of our estimators under general conditions that allow for weak correlations across time, rows, or columns of the noise. A novel approach is introduced to overcome rotational ambiguity in the estimators, enhancing the clarity and interpretability of the estimated loading matrices. Our simulation study highlights the merits of the proposed estimators and the effective of the smoothing operation. In an application to international trade flow, we investigate the trading hubs, centrality, patterns, and trends in the trading network.