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

TL;DR

This paper introduces a novel continuous-time Le9vy-driven graph Ornstein-Uhlenbeck model for edge-indexed network time series, enhancing modeling flexibility and forecasting accuracy in complex network data.

Contribution

It extends GNAR processes to continuous time with graph OU dynamics, accommodating Le9vy noise and providing maximum-likelihood estimation with proven asymptotic properties.

Findings

Model captures both Brownian and jump behaviors.

Improves forecasting accuracy over benchmarks.

Reduces computational time in empirical applications.

Abstract

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.