Interpretable Time Series Autoregression for Periodicity Quantification

TL;DR

This paper introduces sparse autoregression models with mixed-integer optimization for interpretable and scalable analysis of periodicity in complex spatiotemporal time series, validated on mobility and climate data.

Contribution

It proposes novel scalable MIO-based sparse autoregression models for both stationary and non-stationary time series, enabling interpretable periodicity quantification.

Findings

Revealed daily and weekly cycles in NYC ridesharing data.

Uncovered evolving spatial temperature patterns over decades.

Detected global sea surface temperature dynamics, including El Niño.

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.