Sequential change point detection in high dimensional time series
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Change point detection in high dimensional data has found considerable interest interest in recent years. Most of the literature designs methodology for a retrospective analysis, where the whole sample is already available when the statistical inference begins. This paper develops monitoring schemes for the online scenario, where high dimensional data arrives steadily and changes shall be detected as fast as possible controlling at the same time the probability of a false alarm. We develop sequential procedures capable of detecting changes in the mean vector of a successively observed high dimensional time series with spatial and temporal dependence. In a high dimensional scenario it is shown that the new monitoring schemes have asymptotic level alpha under the null hypothesis of no change and are consistent under the alternative of a change in at least one component. The properties of the new methodology are illustrated by means of a simulation study and in the analysis of a data example. As a side result, we show that the range of a Brownian motion is in the domain of attraction of the Gumbel distribution.
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