Exploring the ability of the Pettitt method for detecting change point by Monte Carlo simulation

Abstract

The Pettitt method, which is a rank-based test method, has been widely used to detect change point in the mean value of observed series. Traditionally the rank-based test has been assumed to be distribution-free and not sensitive to outliers and skewed distributions. However, there has no evidence provided to prove this assumption. Based on the work of Yue and Wang (Stoch Environ Res Risk Assess 16:307–323, 2002), this study defines the success rate of detecting the given change point as the ability of the Pettitt method, and investigates the ability in various circumstances by means of Monte Carlo simulation. Experiment results demonstrate that, the ability of the Pettitt method depends on not only the pre-assigned significance level, but also various properties of the sample data, including the sample size, the magnitude of a shift and the change point position. Besides, the distribution type and the distribution parameters such as the coefficient of variation, the coefficient of skewness and the shape parameter also seriously influence the ability. As expected, it is easier for the method to detect the change point when the sample size is larger, or the magnitude of a change point is bigger, or the variation of the sample data is smaller. And the highest ability is obtained when the change point occurs at the middle position of the series. These simulation results would provide users an extensive and detailed understanding about the use of the Pettitt method for the detection of change point.