Building confidence curves with classical change point tests

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.

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.