Likelihood theory for the Graph Ornstein-Uhlenbeck process
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Author(s)
Courgeau, Valentin
Veraart, Almut
Type
Journal Article
Abstract
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.
Date Issued
2022-07-01
Date Acceptance
2021-08-21
Citation
Statistical Inference for Stochastic Processes: an international journal devoted to time series analysis and the statistics of continuous time processes and dynamical systems, 2022, 25, pp.227-260
ISSN
1387-0874
Publisher
Springer
Start Page
227
End Page
260
Journal / Book Title
Statistical Inference for Stochastic Processes: an international journal devoted to time series analysis and the statistics of continuous time processes and dynamical systems
Volume
25
Copyright Statement
© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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Subjects
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Ornstein-Uhlenbeck processes
Multivariate Levy process
Continuous-time likelihood
Maximum likelihood estimator
Graphical modelling
Central limit theorem
Adaptive Lasso
VOLATILITY MATRIX ESTIMATION
DRIVEN
DISTRIBUTIONS
ERGODICITY
COVARIANCE
STATISTICS
MODELS
Statistics & Probability
0104 Statistics
Publication Status
Published
Date Publish Online
2021-10-21