### Abstract

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 |
---|---|

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 |

### Fingerprint

### 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

*Econometric Theory*,

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

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

Research output: Contribution to journal › Article

*Econometric Theory*, vol. 33, no. 6, pp. 1352-1386. https://doi.org/10.1017/S026646661600044X

}

TY - JOUR

T1 - Testing for changes in Kendall’s tau

AU - Dehling, Herold

AU - Vogel, Daniel

AU - Wendler, Martin

AU - Wied, Dominik

PY - 2017/12

Y1 - 2017/12

N2 - 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 absolutelyregular 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.

AB - 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 absolutelyregular 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.

KW - change-point analysis

KW - Kendall's tau

KW - U-statistic

KW - functional limit theorem

KW - near epoch dependence in probability

U2 - 10.1017/S026646661600044X

DO - 10.1017/S026646661600044X

M3 - Article

VL - 33

SP - 1352

EP - 1386

JO - Econometric Theory

JF - Econometric Theory

SN - 0266-4666

IS - 6

ER -