Interpretable Time Series Autoregression for Periodicity Quantification
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916841721430016 |
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| author | Chen, Xinyu Digalakis Jr, Vassilis Ding, Lijun Zhuang, Dingyi Zhao, Jinhua |
| author_facet | Chen, Xinyu Digalakis Jr, Vassilis Ding, Lijun Zhuang, Dingyi Zhao, Jinhua |
| contents | Time series autoregression (AR) is a classical tool for modeling auto-correlations and periodic structures in real-world systems. We revisit this model from an interpretable machine learning perspective by introducing sparse autoregression (SAR), where $\ell_0$-norm constraints are used to isolate dominant periodicities. We formulate exact mixed-integer optimization (MIO) approaches for both stationary and non-stationary settings and introduce two scalable extensions: a decision variable pruning (DVP) strategy for temporally-varying SAR (TV-SAR), and a two-stage optimization scheme for spatially- and temporally-varying SAR (STV-SAR). These models enable scalable inference on real-world spatiotemporal datasets. We validate our framework on large-scale mobility and climate time series. On NYC ridesharing data, TV-SAR reveals interpretable daily and weekly cycles as well as long-term shifts due to COVID-19. On climate datasets, STV-SAR uncovers the evolving spatial structure of temperature and precipitation seasonality across four decades in North America and detects global sea surface temperature dynamics, including El Niño. Together, our results demonstrate the interpretability, flexibility, and scalability of sparse autoregression for periodicity quantification in complex time series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interpretable Time Series Autoregression for Periodicity Quantification Chen, Xinyu Digalakis Jr, Vassilis Ding, Lijun Zhuang, Dingyi Zhao, Jinhua Machine Learning Artificial Intelligence Time series autoregression (AR) is a classical tool for modeling auto-correlations and periodic structures in real-world systems. We revisit this model from an interpretable machine learning perspective by introducing sparse autoregression (SAR), where $\ell_0$-norm constraints are used to isolate dominant periodicities. We formulate exact mixed-integer optimization (MIO) approaches for both stationary and non-stationary settings and introduce two scalable extensions: a decision variable pruning (DVP) strategy for temporally-varying SAR (TV-SAR), and a two-stage optimization scheme for spatially- and temporally-varying SAR (STV-SAR). These models enable scalable inference on real-world spatiotemporal datasets. We validate our framework on large-scale mobility and climate time series. On NYC ridesharing data, TV-SAR reveals interpretable daily and weekly cycles as well as long-term shifts due to COVID-19. On climate datasets, STV-SAR uncovers the evolving spatial structure of temperature and precipitation seasonality across four decades in North America and detects global sea surface temperature dynamics, including El Niño. Together, our results demonstrate the interpretability, flexibility, and scalability of sparse autoregression for periodicity quantification in complex time series. |
| title | Interpretable Time Series Autoregression for Periodicity Quantification |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2506.22895 |