Ratio tests for change point detection

Details Ratio tests for change point detection Ratio tests for change point detection

2008-05-16

arxiv.org/abs/0805.2473v1

IMS Collections 2008, Vol. 1, 293-304

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/193940307000000220 the IMS Collections (http://www.imstat.org/publications/imscollec

Scientific paper

10.1214/193940307000000220

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.

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