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:2022:10.1007/s11203-021-09257-1,
author = {Courgeau, V and Veraart, A},
doi = {10.1007/s11203-021-09257-1},
journal = {Statistical Inference for Stochastic Processes: an international journal devoted to time series analysis and the statistics of continuous time processes and dynamical systems},
pages = {227--260},
title = {Likelihood theory for the Graph Ornstein-Uhlenbeck process},
url = {http://dx.doi.org/10.1007/s11203-021-09257-1},
volume = {25},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We  consider  the  problem  of  modelling  restricted  interactions  between  continuously-observed time series as given by a known static graph (or network) structure.  For thispurpose, we define a parametric multivariate Graph Ornstein-Uhlenbeck (GrOU) processdriven by a general L evy process to study the momentum and network effects amongstnodes,  effects  that  quantify  the  impact  of  a  node  on  itself  and  that  of  its  neighbours,respectively.  We derive the maximum likelihood estimators (MLEs) and their usual prop-erties  (existence,  uniqueness  and  efficiency)  along  with  their  asymptotic  normality  andconsistency.  Additionally, an Adaptive Lasso approach, or a penalised likelihood scheme,infers  both  the  graph  structure  along  with  the  GrOU  parameters  concurrently  and  isshown to satisfy similar properties.  Finally, we show that the asymptotic theory extendsto the case when stochastic volatility modulation of the driving L evy process is considered.
AU  - Courgeau,V
AU  - Veraart,A
DO  - 10.1007/s11203-021-09257-1
EP  - 260
PY  - 2022///
SN  - 1387-0874
SP  - 227
TI  - Likelihood theory for the Graph Ornstein-Uhlenbeck process
T2  - Statistical Inference for Stochastic Processes: an international journal devoted to time series analysis and the statistics of continuous time processes and dynamical systems
UR  - http://dx.doi.org/10.1007/s11203-021-09257-1
UR  - http://hdl.handle.net/10044/1/91465
VL  - 25
ER  -
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