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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2505.15220 |
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| _version_ | 1866913850254688256 |
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| author | Kołodziejski, Kamil |
| author_facet | Kołodziejski, Kamil |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimation methods of Matrix-valued AR model Kołodziejski, Kamil Statistics Theory Machine Learning 62M10 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. |
| title | Estimation methods of Matrix-valued AR model |
| topic | Statistics Theory Machine Learning 62M10 |
| url | https://arxiv.org/abs/2505.15220 |