Nonparametric Methods for Online Changepoint Detection

Changepoints have been extensively analysed in order to identify structural changes in time series data, typically when the data are of known parametric form. This report presents an exploration of methods to detect changepoints in a nonparametric setting, where no assumptions are made with regard to the distributional structure of the data, yet must still maintain a specified level of performance. In particular, the framework of a two-sample hypothesis testing procedure for sequential testing is developed, in which test statistics based on ranks of observations are adapted for changepoint detection. This framework is then extended to consider multiple changepoints and data streams. The characteristics and performance of the testing procedure are analysed by comparing the impact of test statistics in a range of scenarios. Under this framework, it is found that while parametric techniques tend to outperform nonparametric techniques in a Gaussian setting, nonparametric tests are a suitable alternative. In addition, it is found that tests for arbitrary distributional changes are comparable to tests designed to detect changes in location and scale. Overall, the nonparametric hypothesis testing procedure is found to perform well, and represents a logical course of action when performing changepoint analysis on data of no known distributional form, a common scenario that applies to a wide variety of real-world processes.