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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.09542 |
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| _version_ | 1866917076373864448 |
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| author | Li, Jingyang Chen, Yang |
| author_facet | Li, Jingyang Chen, Yang |
| contents | High-dimensional matrix and tensor time series often exhibit local dependency, where each entry interacts mainly with a small neighborhood. Accounting for local interactions in a prediction model can greatly reduce the dimensionality of the parameter space, leading to more efficient inference and more accurate predictions. We propose a Local Interaction Autoregressive (LIAR) framework and study Separable LIAR, a variant with shared row and column components, for high-dimensional matrix/tensor time series forecasting problems. We derive a scalable parameter estimation algorithm via parallel least squares with a BIC-type neighborhood selector. Theoretically, we show consistency of neighborhood selection and derive error bounds for kernel and auto-covariance estimation. Numerical simulations show that the BIC selector recovers the true neighborhood with high success rates, the LIAR achieves small estimation errors, and the forecasts outperform matrix time-series baselines. In real data applications, a Total Electron Content (TEC) case study shows the model can identify localized spatio-temporal propagation and improved prediction as compared with non-local time series prediction models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09542 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local Interaction Autoregressive Model for High Dimension Time Series Data Li, Jingyang Chen, Yang Methodology High-dimensional matrix and tensor time series often exhibit local dependency, where each entry interacts mainly with a small neighborhood. Accounting for local interactions in a prediction model can greatly reduce the dimensionality of the parameter space, leading to more efficient inference and more accurate predictions. We propose a Local Interaction Autoregressive (LIAR) framework and study Separable LIAR, a variant with shared row and column components, for high-dimensional matrix/tensor time series forecasting problems. We derive a scalable parameter estimation algorithm via parallel least squares with a BIC-type neighborhood selector. Theoretically, we show consistency of neighborhood selection and derive error bounds for kernel and auto-covariance estimation. Numerical simulations show that the BIC selector recovers the true neighborhood with high success rates, the LIAR achieves small estimation errors, and the forecasts outperform matrix time-series baselines. In real data applications, a Total Electron Content (TEC) case study shows the model can identify localized spatio-temporal propagation and improved prediction as compared with non-local time series prediction models. |
| title | Local Interaction Autoregressive Model for High Dimension Time Series Data |
| topic | Methodology |
| url | https://arxiv.org/abs/2511.09542 |