Tests for scale changes based on pairwise differences

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dc.contributor.authorGerstenberger, Carina
dc.contributor.authorVogel, Daniel
dc.contributor.authorWendler, Martin
dc.date.accessioned2016-11-24T15:46:45Z
dc.date.available2016-11-24T15:46:45Z
dc.date.issued2016
dc.description.abstractIn many applications it is important to know whether the amount of uctuation in a series of observations changes over time. In this article, we investigate different tests for detecting change in the scale of mean-stationary time series. The classical approach based on the CUSUM test applied to the squared centered, is very vulnerable to outliers and impractical for heavy-tailed data, which leads us to contemplate test statistics based on alternative, less outlier-sensitive scale estimators. It turns out that the tests based on Gini's mean difference (the average of all pairwise distances) or generalized Qn estimators (sample quantiles of all pairwise distances) are very suitable candidates. They improve upon the classical test not only under heavy tails or in the presence of outliers, but also under normality. An explanation for this counterintuitive result is that the corresponding long-run variance estimates are less affected by a scale change than in the case of the sample-variance-based test. We use recent results on the process convergence of U-statistics and U-quantiles for dependent sequences to derive the limiting distribution of the test statistics and propose estimators for the long-run variance. We perform a simulation study to investigate the finite sample behavior of the tests and their power. Furthermore, we demonstrate the applicability of the new change-point detection methods at two real-life data examples from hydrology and finance.en
dc.identifier.urihttp://hdl.handle.net/2003/35630
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-17671
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB823;82, 2016en
dc.subjectasymptotic relative efficiencyen
dc.subjectU-statisticen
dc.subjectU-quantileen
dc.subjectQn scale estimatoren
dc.subjectmedian absolute deviationen
dc.subjectlong-run variance estimationen
dc.subjectGini's mean differenceen
dc.subjectchange-point analysisen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleTests for scale changes based on pairwise differencesen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access

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Sonderforschungsbereich (SFB) 823