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In this paper we build on an approach proposed by Zou et al. (2014) fornonpara- metric changepoint detection. This approach defines the bestsegmentation for a data set as the one which minimises a penalised costfunction, with the cost function defined in term of minus a non-parametriclog-likelihood for data within each segment. Min- imising this cost function ispossible using dynamic programming, but their algorithm had a computationalcost that is cubic in the length of the data set. To speed up computation, Zouet al. (2014) resorted to a screening procedure which means that the estimatedsegmentation is no longer guaranteed to be the global minimum of the costfunction. We show that the screening procedure adversely affects the accuracyof the changepoint detection method, and show how a faster dynamic programmingalgorithm, Pruned Exact Linear Time, PELT (Killick et al., 2012), can be usedto find the optimal segmentation with a computational cost that can be close tolinear in the amount of data. PELT requires a penalty to avoidunder/over-fitting the model which can have a detrimental effect on the qualityof the detected changepoints. To overcome this issue we use a relatively newmethod, Changepoints Over a Range of PenaltieS (CROPS) (Haynes et al., 2015),which finds all of the optimal segmentations for multiple penalty values over acontinuous range. We apply our method to detect changes in heart rate duringphysical activity.

A computationally efficient nonparametric approach for changepoint detection