用可解释的稀疏自回归模型量化复杂时间序列中的周期性。
Interpretable Time Series Autoregression for Periodicity Quantification
- 引入$\ ell_0$约束的稀疏自回归，聚焦主导周期。
- 在纽约出行和气候数据中发现日周周期及疫情、厄尔尼诺等长期变化。
- 支持时空变化周期分析，适合需要可解释性的实际场景。
时间序列自回归（AR）是建模现实系统中自相关与周期结构的经典工具。本文从可解释机器学习视角出发，提出稀疏自回归（SAR），通过$\ ell_0$-范数约束识别主导周期性。针对平稳与非平稳情形，构建精确的混合整数优化（MIO）方法，并提出两种可扩展扩展：用于时变SAR（TV-SAR）的决策变量剪枝（DVP）策略，以及用于时空变SAR（STV-SAR）的两阶段优化方案。该框架在大规模时空数据上实现高效推断。在纽约共享出行数据上，TV-SAR揭示了可解释的日/周周期及新冠疫情导致的长期变化；在气候数据中，STV-SAR捕捉了北美洲过去四十年温度与降水季节性的空间演化，并检测到全球海表温度动态，包括厄尔尼诺现象。结果表明，稀疏自回归在周期性量化中具备可解释性、灵活性与可扩展性。
原文摘要 · Abstract (English)
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.
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