Interpretable Time Series Autoregression for Periodicity Quantification
This work provides an interpretable method for periodicity analysis in complex spatiotemporal data, which is incremental as it builds on classical autoregression with new optimization techniques.
The authors tackled the problem of modeling periodic structures in time series by introducing sparse autoregression (SAR) with ℓ₀-norm constraints, enabling interpretable periodicity quantification; they validated it on mobility and climate datasets, revealing daily/weekly cycles and long-term shifts like COVID-19 impacts and El Niño dynamics.
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.