A sequential multiple change-point detection procedure via VIF regression

In this paper, we propose a procedure for detecting multiple change-points in a mean-shift model, where the number of change-points is allowed to increase with the sample size. A theoretic justification for our new method is also given. We first convert the change-point problem into a variable selection problem by partitioning the data sequence into several segments. Then, we apply a modified variance inflation factor regression algorithm to each segment in sequential order. When a segment that is suspected of containing a change-point is found, we use a weighted cumulative sum to test if there is indeed a change-point in this segment. The proposed procedure is implemented in an algorithm which, compared to two popular methods via simulation studies, demonstrates satisfactory performance in terms of accuracy, stability and computation time. Finally, we apply our new algorithm to analyze two real data examples.