November 2022 Rank-based change-point analysis for long-range dependent time series
Annika Betken, Martin Wendler
Author Affiliations +
Bernoulli 28(4): 2209-2233 (November 2022). DOI: 10.3150/21-BEJ1416

Abstract

We consider change-point tests based on rank statistics to test for structural changes in long-range dependent observations. Under the hypothesis of stationary time series and under the assumption of a change with decreasing change-point height, the asymptotic distributions of corresponding test statistics are derived. For this, a uniform reduction principle for the sequential empirical process in a two-parameter Skorohod space equipped with a weighted supremum norm is proved. Moreover, we compare the efficiency of rank tests resulting from the consideration of different score functions. Under Gaussianity, the asymptotic relative efficiency of rank-based tests with respect to the CuSum test is 1, irrespective of the score function. Regarding the practical implementation of rank-based change-point tests, we suggest to combine self-normalized rank statistics with subsampling. The theoretical results are accompanied by simulation studies that, in particular, allow for a comparison of rank tests resulting from different score functions. With respect to the finite sample performance of rank-based change-point tests, the Van der Waerden rank test proves to be favorable in a broad range of situations. Finally, we analyze data sets from economy, hydrology, and network traffic monitoring in view of structural changes and compare our results to previous analysis of the data.

Funding Statement

Research supported by Collaborative Research Center SFB 823 Statistical modelling of nonlinear dynamic processes.
Martin Wendler was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft - DFG), project WE 5988/3 Analyse funktionaler Daten ohne Dimensionsreduktion.

Acknowledgments

The authors would like to thank Prof. Marie Hušková for encouraging research on the considered topic. Moreover, the authors would like to thank the referee, the Associate Editor, and the Editor for comments and suggestions which significantly contributed to improving the quality of the manuscript.

Citation

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Annika Betken. Martin Wendler. "Rank-based change-point analysis for long-range dependent time series." Bernoulli 28 (4) 2209 - 2233, November 2022. https://doi.org/10.3150/21-BEJ1416

Information

Received: 1 October 2020; Published: November 2022
First available in Project Euclid: 17 August 2022

zbMATH: 07594057
MathSciNet: MR4474541
Digital Object Identifier: 10.3150/21-BEJ1416

Keywords: Asymptotic relative efficiency , Change-point , empirical process , long memory , rank statistic , self-normalization , subsampling

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Vol.28 • No. 4 • November 2022
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