# Online Topology Identification from Vector Autoregressive Time Series

arXiv: https://arxiv.org/abs/1904.01864 · HTML: https://mlsanity.com/paper/1904.01864/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2019.

## Built on by (most cited first, 9 of 9)

- [Learning Time-Varying Graphs from Online Data](https://mlsanity.com/paper/2110.11017/) (2021)
- [Structural Knowledge Informed Continual Multivariate Time Series Forecasting](https://mlsanity.com/paper/2402.12722/) (2024)
- [Explainable nonlinear modelling of multiple time series with invertible neural networks](https://mlsanity.com/paper/2107.00391/) (2021)
- [Online Graph Learning in Dynamic Environments](https://mlsanity.com/paper/2110.05023/) (2021)
- [Online Graph Topology Learning via Time-Vertex Adaptive Filters: From Theory to Cardiac Fibrillation](https://mlsanity.com/paper/2411.01567/) (2024)
- [Random Feature Approximation for Online Nonlinear Graph Topology Identification](https://mlsanity.com/paper/2110.09935/) (2021)
- [Efficient Interpretable Nonlinear Modeling for Multiple Time Series](https://mlsanity.com/paper/2309.17154/) (2023)
- [Role-Specific Predictive Geometries for Nonstationary Multivariate Graph-Signal Forecasting](https://mlsanity.com/paper/2609.06519/) (2026)
- [AeroChem: Closed-loop Physics-Informed State Space Modeling for Long-term Chemically-Reactive Air Quality Forecasting--Extended Version](https://mlsanity.com/paper/2610.16630/) (2026)

## Abstract (arXiv)

Causality graphs are routinely estimated in social sciences, natural sciences, and engineering due to their capacity to efficiently represent the spatiotemporal structure of multivariate data sets in a format amenable for human interpretation, forecasting, and anomaly detection. A popular approach to mathematically formalize causality is based on vector autoregressive (VAR) models and constitutes an alternative to the well-known, yet usually intractable, Granger causality. Relying on such a VAR causality notion, this paper develops two algorithms with complementary benefits to track time-varying causality graphs in an online fashion. Their constant complexity per update also renders these algorithms appealing for big-data scenarios. Despite using data sequentially, both algorithms are shown to asymptotically attain the same average performance as a batch estimator which uses the entire data set at once. To this end, sublinear (static) regret bounds are established. Performance is also characterized in time-varying setups by means of dynamic regret analysis. Numerical results with real and synthetic data further support the merits of the proposed algorithms in static and dynamic scenarios.