Detecting multiple change points: the PULSE criterion

To avoid either intensive computation exhaustive search-based optimization algorithms may have or false positive problem hypothesis testing-based procedures encounter, we in this paper revisit change points detection of means and of variances in a sequence of observations and propose a novel criterion by a signal statistic to define consistent estimation even when the number of change points can go to infinity at a certain rate as the sample size goes to infinity. The signal statistic exhibits a useful”PULSE” pattern near change points such that we can simultaneously identify all change points. The estimation consistency can hold for the number of change points and for locations in a certain sense. Further, because of its visualization nature, in practice, the locations can also be relatively more easily identified by plots than existing methods in the literature. The method can also detect weak signals in the sense that those changes go to zero. As a generic methodology, it may be extendable to handle with other models. The numerical studies we conduct validate its good performance.