### 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.

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 language | English |
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Pages (from-to) | 1352-1386 |

Number of pages | 35 |

Journal | Econometric Theory |

Volume | 33 |

Issue number | 6 |

Early online date | 4 Nov 2016 |

DOIs | |

Publication status | Published - Dec 2017 |

### Keywords

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

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## Cite this

Dehling, H., Vogel, D., Wendler, M., & Wied, D. (2017). Testing for changes in Kendall’s tau.

*Econometric Theory*,*33*(6), 1352-1386. https://doi.org/10.1017/S026646661600044X