Sequential change point detection in high dimensional time series

Change point detection in high dimensional data has found considerable interest recent years. Most of the literature either designs methodology for a retrospective analysis, where whole sample is already available when statistical inference begins, or considers online schemes controlling average time until false alarm. This paper takes different view and develops monitoring scenario, arrives successively goal to detect changes as fast possible at same probability type I error We develop sequential procedure capable detecting mean vector observed series with spatial temporal dependence. The properties method are analyzed case both, size dimension tend infinity. In this it shown that new scheme asymptotic level alpha under null hypothesis no change consistent alternative least one component vector. approach based on one-dimensional which turns out be often more powerful than usually used CUSUM Page-CUSUM methods, component-wise statistics aggregated by maximum statistic. For analysis our we prove range Brownian motion given interval domain attraction Gumbel distribution, result independent extreme value theory. finite illustrated means simulation study example.