Nonparametric sequential change-point detection for multivariate time series based on empirical distribution functions

Abstract

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 contemporary 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.