High-dimensional cointegration and Kuramoto systems

TL;DR

This paper introduces a new estimator for high-dimensional cointegrated processes with symmetry and low rank restrictions, discusses rank estimation issues, and applies these methods to Kuramoto systems to infer network structures.

Contribution

It proposes a novel estimator for restricted high-dimensional cointegration and explores rank estimation via bootstrap, with applications to Kuramoto systems for network inference.

Findings

Classical rank tests underestimate true rank in high dimensions

New estimator effectively captures symmetry and low rank restrictions

Successful inference of network structure in Kuramoto systems

Abstract

This paper presents a novel estimator for a non-standard restriction to both symmetry and low rank in the context of high dimensional cointegrated processes. Furthermore, we discuss rank estimation for high dimensional cointegrated processes by restricted bootstrapping of the Gaussian innovations. We demonstrate that the classical rank test for cointegrated systems is prone to underestimate the true rank and demonstrate this effect in a 100 dimensional system. We also discuss the implications of this underestimation for such high dimensional systems in general. Also, we define a linearized Kuramoto system and present a simulation study, where we infer the cointegration rank of the unrestricted $p\times p$ system and successively the underlying clustered network structure based on a graphical approach and a symmetrized low rank estimator of the couplings derived from a reparametrization of the likelihood under this unusual restriction.