Tensor Stochastic Regression for High-dimensional Time Series via CP Decomposition
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916784253173760 |
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| author | Li, Shibo Zheng, Yao |
| author_facet | Li, Shibo Zheng, Yao |
| contents | As tensor-valued data become increasingly common in time series analysis, there is a growing need for flexible and interpretable models that can handle high-dimensional predictors and responses across multiple modes. We propose a unified framework for high-dimensional tensor stochastic regression based on CANDECOMP/PARAFAC (CP) decomposition, which encompasses vector, matrix, and tensor responses and predictors as special cases. Tensor autoregression naturally arises as a special case within this framework. By leveraging CP decomposition, the proposed models interpret the interactive roles of any two distinct tensor modes, enabling dynamic modeling of input-output mechanisms. We develop both CP low-rank and sparse CP low-rank estimators, establish their non-asymptotic error bounds, and propose an efficient alternating minimization algorithm for estimation. Simulation studies confirm the theoretical properties and demonstrate the computational advantage. Applications to mixed-frequency macroeconomic data and spatio-temporal air pollution data reveal interpretable low-dimensional structures and meaningful dynamic dependencies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor Stochastic Regression for High-dimensional Time Series via CP Decomposition Li, Shibo Zheng, Yao Methodology As tensor-valued data become increasingly common in time series analysis, there is a growing need for flexible and interpretable models that can handle high-dimensional predictors and responses across multiple modes. We propose a unified framework for high-dimensional tensor stochastic regression based on CANDECOMP/PARAFAC (CP) decomposition, which encompasses vector, matrix, and tensor responses and predictors as special cases. Tensor autoregression naturally arises as a special case within this framework. By leveraging CP decomposition, the proposed models interpret the interactive roles of any two distinct tensor modes, enabling dynamic modeling of input-output mechanisms. We develop both CP low-rank and sparse CP low-rank estimators, establish their non-asymptotic error bounds, and propose an efficient alternating minimization algorithm for estimation. Simulation studies confirm the theoretical properties and demonstrate the computational advantage. Applications to mixed-frequency macroeconomic data and spatio-temporal air pollution data reveal interpretable low-dimensional structures and meaningful dynamic dependencies. |
| title | Tensor Stochastic Regression for High-dimensional Time Series via CP Decomposition |
| topic | Methodology |
| url | https://arxiv.org/abs/2506.06919 |