Estimation methods of Matrix-valued AR model

TL;DR

This paper introduces new estimation techniques for Matrix Autoregressive models, adapting classical methods like Yule-Walker and Burg's to improve efficiency and interpretability in high-dimensional time series analysis.

Contribution

It develops novel estimation methods for MAR models based on Yule-Walker and Burg's approaches, addressing limitations of existing techniques and enhancing model efficiency.

Findings

MAR models with proposed estimators achieve comparable fit to VAR models

The methods provide efficient and interpretable modeling of complex temporal data

Empirical results validate the effectiveness of the new estimation techniques

Abstract

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.