Interpretable Time Series Autoregression for Periodicity Quantification

• URL: http://arxiv.org/abs/2506.22895v2
• Date: Sun, 13 Jul 2025 21:53:21 GMT
• Title: Interpretable Time Series Autoregression for Periodicity Quantification
• Authors: Xinyu Chen, Vassilis Digalakis Jr, Lijun Ding, Dingyi Zhuang, Jinhua Zhao,
• Abstract summary: Time series autoregression (AR) is a classical tool for auto-correlations and periodic structures in real-world systems.<n>We revisit this model by introducing sparse autoregression (SAR), where $ell$-norm constraints are used to isolate dominant periodicities.<n>We validate our framework on large-scale mobility and climate time series.
• Score: 18.6300875919604
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 Ni\~no. Together, our results demonstrate the interpretability, flexibility, and scalability of sparse autoregression for periodicity quantification in complex time series.

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