Statistical inference for Levy-driven graph supOU processes: From short- to long-memory in high-dimensional time series

TL;DR

This paper introduces Levy-driven graph supOU processes for high-dimensional time series, unifying short- and long-range dependence modeling with a new estimation method, validated through simulations and an application to European wind data.

Contribution

The paper develops a novel Levy-driven graph supOU process model that captures dependence structures and provides a consistent, asymptotically normal estimation method, with practical applications.

Findings

The estimator performs well in finite samples.

The model effectively captures dependence in high-dimensional data.

Application demonstrates relevance to energy network analysis.

Abstract

This article introduces Levy-driven graph supOU processes, a parsimonious parametrisation for high-dimensional time series in which dependence between components is governed by a graph structure. Specifically, the model bridges short- and long-range dependence within a single parametric family while accommodating a wide range of marginal distributions. We further develop a generalised method of moments estimator, establish its consistency and asymptotic normality, and assess its finite-sample performance through a simulation study. Finally, we illustrate the practical relevance of our model and estimation method in an empirical study of wind capacity factors in a European electricity network context.