Estimation methods of Matrix-valued AR model

• URL: http://arxiv.org/abs/2505.15220v1
• Date: Wed, 21 May 2025 07:47:05 GMT
• Title: Estimation methods of Matrix-valued AR model
• Authors: Kamil Kołodziejski,
• Abstract summary: This article proposes novel estimation methods for the Matrix Autoregressive (MAR) model.<n>The MAR model offers a parsimonious, yet effective, alternative for high-dimensional time series.<n> 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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