Edge-indexed network time series with graph Ornstein-Uhlenbeck dynamics

We introduce a class of L\'evy-driven graph Ornstein-Uhlenbeck (grOU) models for edge-indexed network time series. The proposed framework extends generalized network autoregressive (GNAR) processes for edge-indexed network time series to continuous time and adapts graph Ornstein-Uhlenbeck dynamics, originally developed for node-indexed processes, to the edge-indexed setting. The model accommodates general L\'evy noise and therefore captures both Brownian and jump behavior. We show that the model parameters can be estimated via a maximum-likelihood framework and derive the asymptotic properties of the estimator. We examine the finite-sample performance of the methodology through simulation studies and illustrate its practical relevance in an empirical application to high-frequency financial data. The results indicate that grOU models for edge-indexed network time series improve forecasting accuracy and reduce computational time relative to standard benchmarks while maintaining robustness through their network-based parametrization.