Consistent community recovery in stochastic block Ornstein-Uhlenbeck processes

Abstract

We propose the stochastic block Ornstein-Uhlenbeck (SBOU) process, a continuous-time multivariate model in which the drift matrix encodes a latent group structure among its components. Our main contribution is a community-detection algorithm whose misclassification proportion converges to zero in a regime combining infill, long-span, and high-dimensional asymptotics. To our knowledge, this is the first consistency result of this kind for latent group recovery in a discretely observed continuous-time multivariate model. As a key intermediate result, we establish consistency of the discretely observed maximum likelihood estimator of the drift matrix in the same regime, thereby extending the high-dimensional L\'evy-driven Ornstein-Uhlenbeck literature. For practical implementation, we develop a feasible model-selection procedure for estimating the support of the drift matrix, which enables data-driven selection of the number of latent groups. The SBOU framework can be viewed as a continuous-time generalisation of the discrete-time stochastic-block VAR model, allowing for both positive and negative dynamic interactions between groups as opposed to only positive. We illustrate the methodology on the RE-Europe wind-capacity dataset and recover a country-level grouping consistent with the geographic benchmark.