Introduction

Many time series are characterised by abrupt changes in structure, such as sudden jumps in level or volatility. We consider changepoints to be those time points which divide a dataset into distinct homogeneous segments. In practice the number of changepoints will not be known. The ability to detect changepoints is important for both methodological and practical reasons including: the validation of an untested scientific hypothesis [27]; monitoring and assessment of safety critical processes [14]; and the validation of modelling assumptions [21].

The development of inference methods for changepoint problems is by no means a recent phenomenon, with early works including [39], [45] and [28]. Increasingly the ability to detect changepoints quickly and accurately is of interest to a wide range of disciplines. Recent examples of application areas include numerous bioinformatic applications [37, 15], the detection of malware within software [51], network traffic analysis [35], finance [46], climatology [32] and oceanography [34].

In this chapter we describe and compare a number of different approaches for estimating changepoints. For a more general overview of changepoint methods, we refer interested readers to [8] and [11]. The structure of this chapter is as follows. First we introduce the model we focus on. We then describe methods for detecting a single changepoint and methods for detecting multiple changepoint, which will cover both frequentist and Bayesian approaches.