High-frequency Estimation of the L\'evy-driven Graph Ornstein-Uhlenbeck process

TL;DR

This paper develops high-frequency estimators for the Lévy-driven Graph Ornstein-Uhlenbeck process, demonstrating their asymptotic properties and applying them to wind capacity data across multiple locations, outperforming traditional methods.

Contribution

Introduces discretized maximum likelihood estimators for the GrOU process with high-frequency data, establishing their asymptotic normality under various jump activities and enabling sparse inference on graph edges.

Findings

Estimators are asymptotically normal under high-frequency sampling.

Stable convergence allows for edge pruning without losing asymptotic properties.

Simulation results show estimators outperform least squares in various graph and noise settings.

Abstract

We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a non-uniform discrete time grid and introduce discretised maximum likelihood estimators with parameters specific to the whole graph or specific to each component, or node. Under a high-frequency sampling scheme, we study the asymptotic behaviour of those estimators as the mesh size of the observation grid goes to zero. We prove two stable central limit theorems to the same distribution as in the continuously-observed case under both finite and infinite jump activity for the L\'evy driving noise. When a graph structure is not explicitly available, the stable convergence allows to consider purpose-specific sparse inference procedures, i.e. pruning, on the edges themselves in parallel to the GrOU inference and preserve its asymptotic properties. We apply the new estimators to wind capacity factor measurements, i.e. the ratio between the wind power produced locally compared to its rated peak power, across fifty locations in Northern Spain and Portugal. We show the superiority of those estimators compared to the standard least squares estimator through a simulation study extending known univariate results across graph configurations, noise types and amplitudes.