Moving Sum Procedure for Change Point Detection under Piecewise Linearity

Abstract

We propose a computationally and statistically efficient procedure for segmenting univariate data under piecewise linearity. The proposed moving sum (MOSUM) methodology detects multiple change points where the underlying signal undergoes discontinuous jumps and/or slope changes. It controls the family-wise error rate at a given significance level and achieves consistency in multiple change point detection, with a minimax optimal estimation rate when the signal is piecewise linear and continuous, all under weak assumptions permitting serial dependence and heavy-tailedness. Computationally, the complexity of the MOSUM procedure is O(n), which, combined with its good performance on simulated datasets, makes it highly attractive compared to the existing methods. We further demonstrate its good performance on a real data example on rolling element-bearing prognostics.