Electronic Journal of Statistics

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

Johannes Tewes

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1496217654

Digital Object Identifier
doi:10.1214/17-EJS1285

Mathematical Reviews number (MathSciNet)
MR3656905

Zentralblatt MATH identifier
1364.62110

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

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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