Robust and nonparametric detection of change-points in time series using U-statistics and U-quantiles

Tests for detecting change-points in weakly dependent (more precisely: near epoch dependent) time series are studied. As examples, we will be able to treat most standard models of time series analysis, such as ARMA and GARCH processes. The presentation will give certain emphasis to the basic problem of testing for an abrupt shift in location, but other questions like a change in variability will also be considered. The popular CUSUM test is not robust to outliers and can be improved in case of non-normal data, particularly for heavy-tails. The CUSUM test can be modified using the Hodges-Lehmann 2-sample estimator, which is the median of all pairwise differences between the samples. It is highly robust and has a high efficiency under normality. Like for a related test based on the 2-sample Wilcoxon statistic, the asymptotics of the Hodges-Lehmann change-point test can be established under general conditions without any moment assumptions. Both tests offer similar power against shifts in the center of the data, but the test based on the Hodges-Lehmann estimator performs superior if a shift occurs far from the center. MOSUM-type tests restrict attention to data in two subsequent moving time windows.  This may overcome possible masking effects due to several shifts into different directions. The talk investigates CUSUM- and MOSUM-type tests based on the 2-sample Wilcoxon statistic or the Hodges-Lehmann estimator by analyzing asymptotical properties and by comparing the performance in finite samples via simulation experiments.