Testing for changes in Kendall’s tau

Herold Dehling, Daniel Vogel, Martin Wendler, Dominik Wied

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18 Citations (Scopus)
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For a bivariate time series ((Xi, Yi))i=1,...,n we want to detect whether the correlation between Xi and Yi stays constant for all i = 1, . . . , n. We propose a nonparametric change-point test statistic based on Kendall’s tau. The asymptotic distribution under the null hypothesis of no change follows from a new U-statistic invariance principle for dependent processes. Assuming a single change-point, we show that the location of the change-point is consistently estimated. Kendall’s tau possesses a high efficiency at the normal distribution, as compared to the normal maximum likelihood estimator, Pearson’s moment correlation. Contrary to Pearson’s correlation coefficient, it shows no loss in efficiency at heavy-tailed distributions, and is therefore particularly suited for financial data, where heavy tails are common. We assume the data ((Xi, Yi))i=1,...,n to be stationary and P-near epoch dependent on an absolutely
regular process. The P-near epoch dependence condition constitutes a generalization of the usually considered Lp-near epoch dependence allowing for arbitrarily heavy-tailed data. We investigate the test numerically, compare it to previous proposals, and illustrate its application with two real-life data examples.
Original languageEnglish
Pages (from-to)1352-1386
Number of pages35
JournalEconometric Theory
Issue number6
Early online date4 Nov 2016
Publication statusPublished - Dec 2017


  • change-point analysis
  • Kendall's tau
  • U-statistic
  • functional limit theorem
  • near epoch dependence in probability


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