  The aim of sequential change-point detection is to issue an alarm when it is
thought that certain probabilistic properties of the monitored observations
have changed. This work is concerned with nonparametric, closed-end testing
procedures based on differences of empirical distribution functions that are
designed to be particularly sensitive to changes in the comtemporary
distribution of multivariate time series. The proposed detectors are
adaptations of statistics used in a posteriori (offline) change-point testing
and involve a weighting allowing to give more importance to recent
observations. The resulting sequential change-point detection procedures are
carried out by comparing the detectors to threshold functions estimated through
resampling such that the probability of false alarm remains approximately
constant over the monitoring period. A generic result on the asymptotic
validity of such a way of estimating a threshold function is stated. As a
corollary, the asymptotic validity of the studied sequential tests based on
empirical distribution functions is proven when these are carried out using a
dependent multiplier bootstrap for multivariate time series. Large-scale Monte
Carlo experiments demonstrate the good finite-sample properties of the
resulting procedures. The application of the derived sequential tests is
illustrated on financial data.
