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Ratio tests for change point detection

Lajos Horváth, Zsuzsanna Horváth, and Marie Hušková

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Abstract

We propose new tests to detect a change in the mean of a time series. Like many existing tests, the new ones are based on the CUSUM process. Existing CUSUM tests require an estimator of a scale parameter to make them asymptotically distribution free under the no change null hypothesis. Even if the observations are independent, the estimation of the scale parameter is not simple since the estimator for the scale parameter should be at least consistent under the null as well as under the alternative. The situation is much more complicated in case of dependent data, where the empirical spectral density at 0 is used to scale the CUSUM process. To circumvent these difficulties, new tests are proposed which are ratios of CUSUM functionals. We demonstrate the applicability of our method to detect a change in the mean when the errors are AR(1) and GARCH(1, 1) sequences.

Chapter information

Source
N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 293-304

Dates
First available in Project Euclid: 1 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1207058281

Digital Object Identifier
doi:10.1214/193940307000000220

Subjects
Primary: 62F03: Hypothesis testing
Secondary: 62F05: Asymptotic properties of tests

Keywords
AR(1) model GARCH(1, 1) ratio tests structural change weak invariance

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Horváth, Lajos; Horváth, Zsuzsanna; Hušková, Marie. Ratio tests for change point detection. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 293--304, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000220. https://projecteuclid.org/euclid.imsc/1207058281


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