  In this paper, we develop an online change-point detection procedure in the
covariance structure of high-dimensional data. A new stopping rule is proposed
to terminate the process as early as possible when a change in covariance
structure occurs. The stopping rule allows temporal dependence and can be
applied to non-Gaussian data. An explicit expression for the average run length
(ARL) is derived, so that the level of threshold in the stopping rule can be
easily obtained with no need to run time-consuming Monte Carlo simulations. We
also establish an upper bound for the expected detection delay (EDD), the
expression of which demonstrates the impact of data dependence and magnitude of
change in the covariance structure. Simulation studies are provided to confirm
accuracy of the theoretical results. The practical usefulness of the proposed
procedure is illustrated by detecting the change of brain's covariance network
in a resting-state fMRI dataset.
