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TESTING FOR CHANGES IN KENDALL’S TAU

  • Herold Dehling (a1), Daniel Vogel (a2), Martin Wendler (a3) and Dominik Wied (a4)
Abstract

For a bivariate time series ((X i ,Y i )) i=1,...,n , we want to detect whether the correlation between X i and Y i 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 ((X i ,Y i )) 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 L p -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.

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Corresponding author
*Address correspondence to Daniel Vogel, Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, UK; e-mail: daniel.vogel@abdn.ac.uk.
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C. Croux & C. Dehon (2010) Influence functions of the Spearman and Kendall correlation measures. Statistical Methods and Applications 19, 497515.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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