A measure of stationarity in locally stationary processes with applications to testing

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dc.contributor.authorDette, Holger
dc.contributor.authorPreuß, Philip
dc.contributor.authorVetter, Mathias
dc.date.accessioned2010-08-03T12:31:25Z
dc.date.available2010-08-03T12:31:25Z
dc.date.issued2010-08-03
dc.description.abstractIn this paper we investigate the problem of measuring deviations from stationarity in locally stationary time series. Our approach is based on a direct estimate of the L²-distance between the spectral density of the locally stationary process and its best approximation by a spectral density of a stationary process. An explicit expression of the minimal distance is derived, which depends only on integrals of the spectral density of the stationary process and its square. These integrals can be estimated directly without estimating the spectral density, and as a consequence, the estimation of the measure of stationarity does not require the specification of smoothing parameters. We show weak convergence of an appropriately standardized version of the statistic to a standard normal distribution. The results are used to construct confidence intervals for the measure of stationarity and to develop a new test for the hypothesis of stationarity which does not require regularization. Finally, we investigate the finite sample properties of the resulting confidence intervals and tests by means of a small simulation study and illustrate the methodology in three data examples. AMS subject classification: 62M10, 62M15, 62G10en
dc.identifier.urihttp://hdl.handle.net/2003/27323
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-15953
dc.language.isoenen
dc.relation.ispartofseriesDiscussion Paper / SFB 823;32/2010
dc.subjectGoodness-of-fit testen
dc.subjectIntegrated periodogramen
dc.subjectL²-distanceen
dc.subjectLocally stationary processen
dc.subjectNon stationary processen
dc.subjectSpectral densityen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleA measure of stationarity in locally stationary processes with applications to testingen
dc.typeTextde
dc.type.publicationtypereportde
dcterms.accessRightsopen access

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