Testing for changes in Kendall’s tau

Herold Dehling, Daniel Vogel, Martin Wendler, Dominik Wied

Research output: Contribution to journalArticle

4 Citations (Scopus)
8 Downloads (Pure)

Abstract

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
Volume33
Issue number6
Early online date4 Nov 2016
DOIs
Publication statusPublished - Dec 2017

Fingerprint

statistics
efficiency
time series
Change point
Kendall's tau
Testing
Correlation coefficient
Test statistic
U-statistics
Invariance
Maximum likelihood estimator
Normal distribution
Financial data
Heavy tails
Asymptotic distribution
Heavy-tailed distribution

Keywords

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

ASJC Scopus subject areas

  • Economics, Econometrics and Finance(all)
  • Social Sciences(all)

Cite this

Testing for changes in Kendall’s tau. / Dehling, Herold; Vogel, Daniel; Wendler, Martin; Wied, Dominik.

In: Econometric Theory, Vol. 33, No. 6, 12.2017, p. 1352-1386.

Research output: Contribution to journalArticle

Dehling, H, Vogel, D, Wendler, M & Wied, D 2017, 'Testing for changes in Kendall’s tau', Econometric Theory, vol. 33, no. 6, pp. 1352-1386. https://doi.org/10.1017/S026646661600044X
Dehling, Herold ; Vogel, Daniel ; Wendler, Martin ; Wied, Dominik. / Testing for changes in Kendall’s tau. In: Econometric Theory. 2017 ; Vol. 33, No. 6. pp. 1352-1386.
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