Several commonly-used nonparametric change-point detection methods are analysed in terms of power, ability and accuracy of the estimated change-point location. The analysis is performed with synthetic data for different sample sizes, two types of change and different magnitudes of change. The methods studied are the Pettitt method, a method based on the Cramér von Mises (CvM) two-sample test statistic and a variant of the CUSUM method. The methods differ considerably in behaviour. For all methods the spread of estimated change-point location increases significantly for points near one of the ends of the sample. Series of annual maximum runoff for four stations on the Yangtze River in China are used to examine the performance of the methods on real data. It was found that the CvM-based test gave the best results, but all three methods suffer from bias and low detection rates for change points near the ends of the series.

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<p>A necessary first step in any hydrological study is the analysis of the available measurements and in particular their relevance to the future behaviour of the system. Periodic variations and linear trends are of special interest. However, an abrupt change in the system and the statistical processes that affect the measurements will, if uncorrected, interfere with the analysis. Detecting abrupt changes in time  series is therefore of considerable importance. The classical tests are primarily intended to test the null hypothesis “There is no change point”. If there is a change point (CP), then the usual approach reuses the classical test results to find a location. Additional work is then needed to determine the uncertainty in the position.</p><p>In 2018 two new approaches to change point analysis were presented in the statistical literature. One approach uses a deviance function and the other uses homogeneity tests. Both approaches construct confidence sets for the change point location at all confidence levels.  An interesting aspect of these approaches is that they can produce confidence sets, not just confidence intervals. For example,  in a series of annual maxima two points separated by several years may be marked as potential CP at a given confidence level without marking the intervening years as possible CPs at that level. The approach using homogeneity tests was applied to  both synthetic time series and measurement time series. The results for synthetic time series provide information on the statistical properties of the approach for small samples.  The results for measurement time series are compared with the CPs found for these series in the literature.</p>

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In this paper, a method based on Approximate Empirical likelihood ratio and a Deviance function combined with bootstrapping (AED-BP) is proposed to construct a confidence curve for the location of a change point. The method is compared with a method based on parametric Profile Likelihood and a Deviance function combined with Monte Carlo simulation (PLD-MC). A confidence curve provides a representation of the uncertainty in the outcome of the change point analysis. To evaluate the practical usability of confidence curves constructed by AED-BP, its properties were examined and its performance was compared to that of PLD-MC. The methods were applied to both synthetic and real data. Synthetic data were generated from three parametric distributions: Fréchet with a constant shape parameter, log-normal, and gamma distributions. The real data are the hydrometeorological data analysed in other studies. The change points found in the original publications are used as a reference in this present paper. The results show that AED-BP has a performance that is similar to PLD-MC, but has an advantage in that it is not necessary to select a distribution family for the data. The AED-BP results on the Annual Maximum Runoff series for the stations Yichang and Hankou along the Yangtze river are among the first that show a possible effect of the presence of the Three Gorges dam.