## Electronic Journal of Statistics

### Power of change-point tests for long-range dependent data

#### Abstract

We investigate the power of the CUSUM test and the Wilcoxon change-point tests for a shift in the mean of a process with long-range dependent noise. We derive analytic formulas for the power of these tests under local alternatives. These results enable us to calculate the asymptotic relative efficiency (ARE) of the CUSUM test and the Wilcoxon change point test. We obtain the surprising result that for Gaussian data, the ARE of these two tests equals $1$, in contrast to the case of i.i.d. noise when the ARE is known to be $3/\pi$.

#### Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 2168-2198.

Dates
First available in Project Euclid: 19 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1495159237

Digital Object Identifier
doi:10.1214/17-EJS1283

Mathematical Reviews number (MathSciNet)
MR3654823

Zentralblatt MATH identifier
1378.62064

#### Citation

Dehling, Herold; Rooch, Aeneas; Taqqu, Murad S. Power of change-point tests for long-range dependent data. Electron. J. Statist. 11 (2017), no. 1, 2168--2198. doi:10.1214/17-EJS1283. https://projecteuclid.org/euclid.ejs/1495159237

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