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A robust method for shift detection in time series

Author

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  • H Dehling
  • R Fried
  • M Wendler

Abstract

SummaryWe present a robust and nonparametric test for the presence of a changepoint in a time series, based on the two-sample Hodges–Lehmann estimator. We develop new limit theory for a class of statistics based on two-sample U-quantile processes in the case of short-range dependent observations. Using this theory, we derive the asymptotic distribution of our test statistic under the null hypothesis of a constant level. The proposed test shows better overall performance under normal, heavy-tailed and skewed distributions than several other modifications of the popular cumulative sums test based on U-statistics, one-sample U-quantiles or M-estimation. The new theory does not involve moment conditions, so any transform of the observed process can be used to test the stability of higher-order characteristics such as variability, skewness and kurtosis.

Suggested Citation

  • H Dehling & R Fried & M Wendler, 2020. "A robust method for shift detection in time series," Biometrika, Biometrika Trust, vol. 107(3), pages 647-660.
    • Handle: RePEc:oup:biomet:v:107:y:2020:i:3:p:647-660.
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    File URL: http://hdl.handle.net/10.1093/biomet/asaa004
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