  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.
