On change-points tests based on two-samples U-Statistics for weakly dependent observations

• Published in: Statistical papers (Berlin, Germany) Vol. 63; no. 1; pp. 287 - 316
• Main Authors: Ngatchou-Wandji, Joseph, Elharfaoui, Echarif, Harel, Michel
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-02-2022; Springer Nature B.V; Springer Verlag
• Subjects: Applications; Asymptotic properties; Change detection; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Hypotheses; Insurance; Management; Mathematics; Mathematics and Statistics; Methodology; Null hypothesis; Operations Research/Decision Theory; Probability Theory and Stochastic Processes; Regular Article; Statistical analysis; Statistical methods; Statistical tests; Statistics; Statistics for Business; Statistics Theory; 62M10; 60F17; 62F03
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-021-01242-3

We study change-points tests based on
U
-statistics for absolutely regular observations. Our method avoids some technical assumptions on the data and the kernel. The asymptotic properties of the
U
-statistics are studied under the null hypothesis, under fixed alternatives and under a sequence of local alternatives. The asymptotic distributions of the test statistics under the null hypothesis and under the local alternatives are given explicitly and the tests are shown to be consistent. A small set of simulations is done for evaluating the performance of the tests in detecting changes in the mean, variance and autocorrelation of some simple time series.