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We propose a computationally and statistically efficient procedure forsegmenting univariate data under piecewise linearity. The proposed moving sum(MOSUM) methodology detects multiple change points where the underlying signalundergoes discontinuous jumps and/or slope changes. Theoretically, it controlsthe family-wise error rate at a given significance level asymptotically andachieves consistency in multiple change point detection, as well as matchingthe minimax optimal rate of estimation when the signal is piecewise linear andcontinuous, all under weak assumptions permitting serial dependence andheavy-tailedness. Computationally, the complexity of the MOSUM procedure is$O(n)$ which, combined with its good performance on simulated datasets, makingit highly attractive in comparison with the existing methods. We furtherdemonstrate its good performance on a real data example on rollingelement-bearing prognostics.

Moving sum procedure for change point detection under piecewise linearity