Change-point detection in high-dimensional time series using MOSUM

Music City Center 

In this talk we study the problem of detecting abrupt dense changes in the mean of a high-dimensional time series. We shall focus on the dense change in the sense that a large proportion of the elements in the mean vectors can change, although our method can also handle sparse change if the jump size is large. Specifically we developed a nonparametric methodology to identify the change-point location for a time series with both temporal and cross-sectional dependence. We construct a MOSUM statistic which can also be considered as a trimmed U-statistic for the l_2 norm of the mean change at each location, and the local maximizer of the MOSUM statistics serves as a natural estimator for the true change point location. The limiting distribution of the proposed estimator can be derived, which is a two-sided Brownian motion with a drift. We further compare the constructed MOSOM statistics with some threshold to determine the number of changes points in the data so that the same method can work under both single change point model or multiple change point model. Simulation results show that the method can accurately estimate both the number and the location of change points, and the method is not sensitive to the tuning parameters.

Change-point

high-dimensional time series