Non‐Parametric Change‐Point Tests for Long‐Range Dependent Data

Herold Dehling · Aeneas Rooch · Murad S. Taqqu

82 citations0/0 files storedScandinavian Journal of Statistics

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Advanced Statistical Process Monitoring Statistical Methods and Inference Complex Systems and Time Series Analysis

Abstract

Abstract. We propose a non‐parametric change‐point test for long‐range dependent data, which is based on the Wilcoxon two‐sample test. We derive the asymptotic distribution of the test statistic under the null hypothesis that no change occurred. In a simulation study, we compare the power of our test with the power of a test which is based on differences of means. The results of the simulation study show that in the case of Gaussian data, our test has only slightly smaller power minus.3pt than the ‘difference‐of‐means’ test. For heavy‐tailed data, our test outperforms the ‘difference‐of‐means’ test.

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References

1997Limit theorems in change-point analysis 1979Convergence of integrated processes of arbitrary Hermite rank 2009Break detection in the covariance structure of multivariate time series models 2009Break detection in the covariance structure of multivariate time series models 1997The effect of long-range dependence on change-point estimators

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2021Data segmentation algorithms: Univariate mean change and beyond 2015Threshold models in time series analysis—Some reflections 2014Generalized Hermite processes, discrete chaos and limit theorems 2016Testing for Change‐Points in Long‐Range Dependent Time Series by Means of a Self‐Normalized Wilcoxon Test 2015Change-Point Detection Under Dependence Based on Two-Sample U-Statistics 2017Power of change-point tests for long-range dependent data 2017Detection of a changepoint, a mean-shift accompanied with a trend change, in short time-series with autocorrelation 2020Convergence of U-processes in Hölder spaces with application to robust detection of a changed segment

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