  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. Theoretically, it controls
the family-wise error rate at a given significance level asymptotically and
achieves consistency in multiple change point detection, as well as matching
the minimax optimal rate of estimation 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, making
it highly attractive in comparison with the existing methods. We further
demonstrate its good performance on a real data example on rolling
element-bearing prognostics.
