Ornstein-Uhlenbeck-Lévy Electricity Portfolios with Wind Energy Contracting

Longoria, Genaro; Davy, Alan; Shi, Lei

doi:10.1007/s40866-018-0054-9

Cited by 5 publications

(3 citation statements)

References 31 publications

(39 reference statements)

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“…Ornstein-Uhlenbeck (OU) models, and in particular those driven by Lévy processes, form a class of continuous-time processes with a broad range of applications, e.g. in finance for pairs trading [29,24] and volatility modelling [6,44], in electricity management [34] or neuroscience [42]. On the other hand, the availability of high-dimensional time series datasets gave rise to sparse inference for OU-type processes [12,26,40] as a way to control interactions within complex systems.…”

Section: Introductionmentioning

confidence: 99%

High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

Courgeau

Veraart

2022

Electron. J. Statist.

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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.

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Section: Introductionmentioning

confidence: 99%

High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

Courgeau

Veraart

2022

Electron. J. Statist.

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“…Ornstein-Uhlenbeck (OU) models, driven by Brownian motion or Lévy processes, form a class of continuous-time models with a broad range of applications: in finance for pairs trading (Endres and Stübinger 2019;Holý and Tomanová 2018) and volatility modelling (Barndorff-Nielsen and Shephard 2001;Pigorsch and Stelzer 2009b), in neuroscience (Melanson and Longtin 2019), or even in electricity management (Longoria et al 2018). In parallel, highdimensional time series datasets fostered the development of sparse inference for OU-type processes (Boninsegna et al 2018;Gaïffas and Matulewicz 2019) as a way to control interactions within complex systems.…”

Section: Introductionmentioning

confidence: 99%

Likelihood theory for the graph Ornstein-Uhlenbeck process

Courgeau

Veraart

2021

Stat Inference Stoch Process

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We consider the problem of modelling restricted interactions between continuously-observed time series as given by a known static graph (or network) structure. For this purpose, we define a parametric multivariate Graph Ornstein-Uhlenbeck (GrOU) process driven by a general Lévy process to study the momentum and network effects amongst nodes, 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 properties (existence, uniqueness and efficiency) along with their asymptotic normality and consistency. Additionally, an Adaptive Lasso approach, or a penalised likelihood scheme, infers both the graph structure along with the GrOU parameters concurrently and is shown to satisfy similar properties. Finally, we show that the asymptotic theory extends to the case when stochastic volatility modulation of the driving Lévy process is considered.

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“…Ornstein-Uhlenbeck (OU) models, and in particular those driven by Lévy processes, form a class of continuous-time processes with a broad range of applications, e.g. in finance for pairs trading (Endres & Stbinger 2019, Hol & Tomanov 2018 and volatility modelling (Barndorff-Nielsen & Shephard 2001, Pigorsch & Stelzer 2009, in electricity management (Longoria et al 2018) or neuroscience (Melanson & Longtin 2019). On the other hand, the availability of high-dimensional time series datasets gave rise to sparse inference for OU-type processes (Boninsegna et al 2018, Gaffas & Matulewicz 2019, Matulewicz 2017) as a way to control interactions within complex systems.…”

Section: Introductionmentioning

confidence: 99%

High-frequency Estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

Courgeau¹,

Veraart²

2020

Preprint

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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 highfrequency 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. 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.

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Ornstein-Uhlenbeck-Lévy Electricity Portfolios with Wind Energy Contracting

Cited by 5 publications

References 31 publications

High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

Likelihood theory for the graph Ornstein-Uhlenbeck process

High-frequency Estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

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