Abstract

Recently a new approach to change point analysis was presented in the statistical literature. This approach is based on the construction of confidence sets. One way to apply it is to take existing homogeneity tests as a basis. In this study Pettitt and CUSUM based homogeneity tests are used to derive distribution-free change point analysis methods. These are applied to a large number of synthetic data series, and the results are analyzed. The results are compared to results of the application of the classical Pettitt and CUSUM methods, and with a Bayesian approach. It is shown that the new methods perform as least as well as the classical methods and the Bayesian method. Unlike the classical methods, the Bayesian and confidence set based methods provide information on the uncertainty of the change point location. The methods are tested on normally distributed synthetic time series and on synthetic time series with a type II Generalized Extreme Value distribution.