# Estimation methods of Matrix-valued AR model

arXiv: https://arxiv.org/abs/2505.15220 · HTML: https://mlsanity.com/paper/2505.15220/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 16 references that are in the map.
- First posted on arXiv 21 May 2025.

## Builds on (most cited first, 3 of 3)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Autoregressive Models for Matrix-Valued Time Series](https://mlsanity.com/paper/1812.08916/) (2018)
- [Multi-linear Tensor Autoregressive Models](https://mlsanity.com/paper/2110.00928/) (2021)

## Abstract (arXiv)

This article proposes novel estimation methods for the Matrix Autoregressive (MAR) model, specifically adaptations of the Yule-Walker equations and Burg's method, addressing limitations in existing techniques. The MAR model, by maintaining a matrix structure and requiring significantly fewer parameters than vector autoregressive (VAR) models, offers a parsimonious, yet effective, alternative for high-dimensional time series. Empirical results demonstrate that MAR models estimated via the proposed methods achieve a comparable fit to VAR models across metrics such as MAE and RMSE. These findings underscore the utility of Yule-Walker and Burg-type estimators in constructing efficient and interpretable models for complex temporal data.