Robust change-point detection for functional time series based on U-statistics and dependent wild bootstrap

Lea Wegner and Martin Wendler ()
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Lea Wegner: Otto-von-Guericke-Universität Magdeburg
Martin Wendler: Otto-von-Guericke-Universität Magdeburg

Statistical Papers, 2024, vol. 65, issue 7, No 26, 4767-4810

Abstract: Abstract The aim of this paper is to develop a change-point test for functional time series that uses the full functional information and is less sensitive to outliers compared to the classical CUSUM test. For this aim, the Wilcoxon two-sample test is generalized to functional data. To obtain the asymptotic distribution of the test statistic, we prove a limit theorem for a process of U-statistics with values in a Hilbert space under weak dependence. Critical values can be obtained by a newly developed version of the dependent wild bootstrap for non-degenerate 2-sample U-statistics.

Keywords: 62R10; 62G35; 62M10; 62F40 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-024-01577-7

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