Detection of Undocumented Changepoints Using Multiple Test Statistics and Composite Reference Series

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Abstract
An evaluation of three hypothesis test statistics that are commonly used in the detection of undocumented changepoints is described. The goal of the evaluation was to determine whether the use of multiple tests could improve undocumented, artificial changepoint detection skill in climate series. The use of successive hypothesis testing is compared to optimal approaches, both of which are designed for situations in which multiple undocumented changepoints may be present. In addition, the importance of the form of the composite climate reference series is evaluated, particularly with regard to the impact of undocumented changepoints in the various component series that are used to calculate the composite. In a comparison of single test changepoint detection skill, the composite reference series formulation is shown to be less important than the choice of the hypothesis test statistic, provided that the composite is calculated from the serially complete and homogeneous component series. However, each of the evaluated composite series is not equally susceptible to the presence of changepoints in its components, which may be erroneously attributed to the target series. Moreover, a reference formulation that is based on the averaging of the first-difference component series is susceptible to random walks when the composition of the component series changes through time (e.g., values are missing), and its use is, therefore, not recommended. When more than one test is required to reject the null hypothesis of no changepoint, the number of detected changepoints is reduced proportionately less than the number of false alarms in a wide variety of Monte Carlo simulations. Consequently, a consensus of hypothesis tests appears to improve undocumented changepoint detection skill, especially when reference series homogeneity is violated. A consensus of successive hypothesis tests using a semihierarchic splitting algorithm also compares favorably to optimal solutions, even when changepoints are not hierarchic.

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