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

by   Valentin Courgeau, et al.

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 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. 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.


Likelihood theory for the Graph Ornstein-Uhlenbeck process

We consider the problem of modelling restricted interactions between con...

Non-Parametric Estimation of Spot Covariance Matrix with High-Frequency Data

Estimating spot covariance is an important issue to study, especially wi...

On the estimation of the jump activity index in the case of random observation times

We propose a nonparametric estimator of the jump activity index β of a p...

Noise Inference For Ergodic Lévy Driven SDE

We study inference for the driving Lévy noise of an ergodic stochastic d...

Flexible nonstationary spatio-temporal modeling of high-frequency monitoring data

Many physical datasets are generated by collections of instruments that ...

Input estimation from discrete workload observations in a Lévy-driven storage system

We consider the estimation of the characteristic exponent of the input t...

Efficient parameter estimation for parabolic SPDEs based on a log-linear model for realized volatilities

We construct estimators for the parameters of a parabolic SPDE with one ...