Imperial College London
Alternate

ProfessorAlmutVeraart

Faculty of Natural Sciences, Department of Mathematics

Head of the Statistics Section, Professor of Statistics
 
 
 
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Contact

 

+44 (0)20 7594 8545a.veraart Website

 
 
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Location

 

551Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Courgeau:2022:10.1214/22-EJS2052,
author = {Courgeau, V and Veraart, A},
doi = {10.1214/22-EJS2052},
journal = {Electronic Journal of Statistics},
pages = {4863--4925},
title = {High-frequency estimation of the Lévy-driven graph Ornstein-Uhlenbeck process},
url = {http://dx.doi.org/10.1214/22-EJS2052},
volume = {16},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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.
AU  - Courgeau,V
AU  - Veraart,A
DO  - 10.1214/22-EJS2052
EP  - 4925
PY  - 2022///
SN  - 1935-7524
SP  - 4863
TI  - High-frequency estimation of the Lévy-driven graph Ornstein-Uhlenbeck process
T2  - Electronic Journal of Statistics
UR  - http://dx.doi.org/10.1214/22-EJS2052
UR  - 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
UR  - http://hdl.handle.net/10044/1/99442
VL  - 16
ER  -
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