Many time series experience abrupt changes in structure. Detecting where these changes in structure, or changepoints, occur is required for effective modelling of the data. In this thesis we explore the common approaches used for detecting changepoints. We focus in particular on techniques which can
be formulated in terms of minimising a cost over segmentations and solved exactly using a class of dynamic programming algorithms. Often implementations of these dynamic programming methods have a computational cost which scales poorly with the length of the time series. Recently pruning ideas have been suggested that can speed up the dynamic programming algorithms, whilst still being guaranteed to be optimal.

In this thesis we extend these methods. First we develop two new algorithms for segmenting piecewise constant data: FPOP and SNIP. We evaluate them against other methods in the literature. We then move on to develop the method OPPL for detecting changes in data subject to fitting a continuous piecewise linear model. We evaluate it against similar methods. We finally extend the OPPL method to deal with penalties that depend on the segment length.