# Interpretable Time Series Autoregression for Periodicity Quantification

arXiv: https://arxiv.org/abs/2506.22895 · HTML: https://mlsanity.com/paper/2506.22895/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 28 Jun 2025.

## Builds on (most cited first, 10 of 10)

- [Best Subset Selection via a Modern Optimization Lens](https://mlsanity.com/paper/1507.03133/) (2015)
- [Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimization](https://mlsanity.com/paper/2004.06152/) (2020)
- [Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization](https://mlsanity.com/paper/2206.00176/) (2022)
- [Rank-one Convexification for Sparse Regression](https://mlsanity.com/paper/1901.10334/) (2019)
- [The Backbone Method for Ultra-High Dimensional Sparse Machine Learning](https://mlsanity.com/paper/2006.06592/) (2020)
- [Slowly Varying Regression under Sparsity](https://mlsanity.com/paper/2102.10773/) (2021)
- [OKRidge: Scalable Optimal k-Sparse Ridge Regression](https://mlsanity.com/paper/2304.06686/) (2023)
- [Time-varying Autoregression with Low Rank Tensors](https://mlsanity.com/paper/1905.08389/) (2019)
- [Discovering Dynamic Patterns from Spatiotemporal Data with Time-Varying Low-Rank Autoregression](https://mlsanity.com/paper/2211.15482/) (2022)
- [Correlating Time Series with Interpretable Convolutional Kernels](https://mlsanity.com/paper/2409.01362/) (2024)

## Built on by (most cited first, 2 of 2)

- [Data-Driven Discovery of Mobility Periodicity for Understanding Urban Systems](https://mlsanity.com/paper/2508.03747/) (2025)
- [TailedTS: Benchmark Dataset for Heavy-Tailed Time Series Prediction and Periodicity Quantification](https://mlsanity.com/paper/2605.16361/) (2026)

## Abstract (arXiv)

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 ℓ0-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.