High-frequency estimation of the Lévy-driven graph Ornstein-Uhlenbeck process
File(s)
Published version
Author(s)
Courgeau, Valentin
Veraart, Almut
Type
Journal Article
Abstract
We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a non-uniform discrete timegrid and introduce discretised maximum likelihood estimators with parameters specific to the whole graph or specific to each component of the graph. 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 Lévy driving noise. In addition to providing the consistency of the estimators, the stable convergence allows us to consider probabilistic sparse inference procedures on the edges themselves when a graph structure is not explicitly available. It also preserves its asymptotic properties. In particular, we also show the asymptotic normality and consistency of an Adaptive Lasso scheme. 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 compare those estimators to the standard least squares estimator through a simulation study extending known univariate results across graph configurations, noise types and amplitudes.
Date Issued
2022-09-27
Date Acceptance
2022-08-23
Citation
Electronic Journal of Statistics, 2022, 16 (2), pp.4863-4925
ISSN
1935-7524
Publisher
Institute of Mathematical Statistics
Start Page
4863
End Page
4925
Journal / Book Title
Electronic Journal of Statistics
Volume
16
Issue
2
Copyright Statement
© 2022 The Author(s). Creative Commons Attribution 4.0 International License.
License URL
Identifier
https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-16/issue-2/High-frequency-estimation-of-the-L%C3%A9vy-driven-Graph-Ornstein-Uhlenbeck/10.1214/22-EJS2052.full
Publication Status
Published
Date Publish Online
2022-09-27