  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.
