High-dimensional change point detection for vector moving average model

This paper investigates single change point detection for the qth-order vector moving average (VMA) model. We perform dimension reduction on the raw data by calculating the weighted sum of the squared differences between the mean vector estimators for each attribute. An additional rectification is further introduced to ensure the statistical properties of the expectation. The change point position is subsequently estimated via the reduced data. Specifically, we construct a CUSUM-type statistic that discards high-order moment terms. The feasibility of the dimension reduction step and the performance of our change point detection approach are validated through various simulated data experiments and real-data analysis.