Electronic Journal of Statistics

Change-point tests under local alternatives for long-range dependent processes

Johannes Tewes

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We consider the change-point problem for the marginal distribution of subordinated Gaussian processes that exhibit long-range dependence. The asymptotic distributions of Kolmogorov-Smirnov- and Cramér-von Mises type statistics are investigated under local alternatives. By doing so we are able to compute the asymptotic relative efficiency of the mentioned tests and the CUSUM test. In the special case of a mean-shift in Gaussian data it is always $1$. Moreover, our theory covers the scenario where the Hermite rank of the underlying process changes.

In a small simulation study, we show that the theoretical findings carry over to the finite sample performance of the tests.

Article information

Electron. J. Statist., Volume 11, Number 1 (2017), 2461-2498.

Received: April 2016
First available in Project Euclid: 31 May 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G20: Asymptotic properties
Secondary: 60F17: Functional limit theorems; invariance principles

Long-range dependence asymptotic relative efficiency empirical process change-point test local alternatives

Creative Commons Attribution 4.0 International License.


Tewes, Johannes. Change-point tests under local alternatives for long-range dependent processes. Electron. J. Statist. 11 (2017), no. 1, 2461--2498. doi:10.1214/17-EJS1285. https://projecteuclid.org/euclid.ejs/1496217654

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