Structural break analysis in high-dimensional covariance structure

TL;DR

This paper introduces a new data-driven method for detecting and localizing abrupt changes in the covariance structure of high-dimensional data, with theoretical guarantees and practical applicability in online settings.

Contribution

It proposes a novel multiscale testing procedure with a calibration scheme for high-dimensional covariance break detection, supported by theoretical analysis.

Findings

Method effectively detects covariance breaks in high-dimensional data

The calibration scheme provides reliable control of false alarms

Simulation results demonstrate practical utility in financial data scenarios

Abstract

We consider detection and localization of an abrupt break in the covariance structure of high-dimensional random data. The paper proposes a novel testing procedure for this problem. Due to its nature, the approach requires a properly chosen critical level. In this regard we propose a purely data-driven calibration scheme. The approach can be straightforwardly employed in online setting and is essentially multiscale allowing for a trade-off between sensitivity and change-point localization (in online setting, the delay of detection). The description of the algorithm is followed by a formal theoretical study justifying the proposed calibration scheme under mild assumption and providing guaranties for break detection. All the theoretical results are obtained in a high-dimensional setting (dimensionality $p >> n$). The results are supported by a simulation study inspired by real-world financial data.