Applying non-negative matrix factorization with covariates to multivariate time series data as a vector autoregression model
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arXiv
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| Format: | Preprint |
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2025
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| author | Satoh, Kenichi |
| author_facet | Satoh, Kenichi |
| contents | We propose a novel framework for analyzing multivariate time series (MTS) data by integrating non-negative matrix factorization (NMF) with vector autoregression (VAR). Termed NMF-VAR, this method models the coefficient matrix of NMF as a VAR process, enabling simultaneous extraction of latent components and temporal dependencies. Unlike standard VAR, which struggles with high dimensionality and lacks clarity, our method introduces a low-rank latent structure that reduces the number of parameters while retaining explanatory power. The proposed framework generalizes the standard VAR model to high-dimensional non-negative data, including the standard VAR as a special case. We formulate the estimation as a constrained optimization problem and present multiplicative update rules for NMF based on existing tri-factorization techniques. We evaluate the method on three real-world datasets: quarterly first-differenced macroeconomic indicators of Canada, monthly international airline passenger volumes, and daily COVID-19 infection counts across Japanese prefectures. The results demonstrate that NMF-VAR effectively captures meaningful patterns such as economic cycles, seasonal travel behavior, and regional epidemic trends. Moreover, the method yields a significant reduction in regression parameters, improving both scalability and model transparency. Overall, NMF-VAR provides an efficient and insightful tool for analyzing high-dimensional and large-scale time series data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Applying non-negative matrix factorization with covariates to multivariate time series data as a vector autoregression model Satoh, Kenichi Methodology We propose a novel framework for analyzing multivariate time series (MTS) data by integrating non-negative matrix factorization (NMF) with vector autoregression (VAR). Termed NMF-VAR, this method models the coefficient matrix of NMF as a VAR process, enabling simultaneous extraction of latent components and temporal dependencies. Unlike standard VAR, which struggles with high dimensionality and lacks clarity, our method introduces a low-rank latent structure that reduces the number of parameters while retaining explanatory power. The proposed framework generalizes the standard VAR model to high-dimensional non-negative data, including the standard VAR as a special case. We formulate the estimation as a constrained optimization problem and present multiplicative update rules for NMF based on existing tri-factorization techniques. We evaluate the method on three real-world datasets: quarterly first-differenced macroeconomic indicators of Canada, monthly international airline passenger volumes, and daily COVID-19 infection counts across Japanese prefectures. The results demonstrate that NMF-VAR effectively captures meaningful patterns such as economic cycles, seasonal travel behavior, and regional epidemic trends. Moreover, the method yields a significant reduction in regression parameters, improving both scalability and model transparency. Overall, NMF-VAR provides an efficient and insightful tool for analyzing high-dimensional and large-scale time series data. |
| title | Applying non-negative matrix factorization with covariates to multivariate time series data as a vector autoregression model |
| topic | Methodology |
| url | https://arxiv.org/abs/2501.17446 |