Online Topology Identification From Vector Autoregressive Time Series

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