This thesis focuses upon the detection and prediction of changepoints in time series. In particular, we develop a range of methods, both parametric and non-parametric, to detect, predict, and forecast in the presence of changepoints. We consider a range of data applications. These include economic, environmental and telematics data sets.

The first part of this thesis concentrates on forecasting. We propose two approaches to incorporate changepoints into the forecasting process. Each of these approaches are flexible. Additionally, we develop methodology to predict future changepoints in a time series. In particular, we can predict changepoints at both future time points, and changes near the end of the time series for which we do not yet have enough observations to detect. This also includes a new approach to pre-whitening time series that accounts for changes in the second order structure of the explanatory time series.

The second part of this thesis is concerned with changepoint detection. We introduce methodology for detecting changes in both the variance and the autocovariance of time series. To do this we consider a local measure of the variance and the autocovariance over time. The approach is non-parametric and resilient to the presence of outliers.