A nonparametric test for stationarity in functional time series

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dc.contributor.authorvan Delft, Anne
dc.contributor.authorBagchi, Pramita
dc.contributor.authorCharaciejus, Vaidotas
dc.contributor.authorDette, Holger
dc.date.accessioned2017-09-06T13:48:08Z
dc.date.available2017-09-06T13:48:08Z
dc.date.issued2017-09-01
dc.description.abstractWe propose a new measure for stationarity of a functional time series, which is based on an explicit representation of the L2-distance between the spectral density operator of a non-stationary process and its best (L2-)approximation by a spectral density operator corresponding to a stationary process. This distance can easily be estimated by sums of Hilbert-Schmidt inner products of periodogram operators (evaluated at different frequencies), and asymptotic normality of an appropriately standardised version of the estimator can be established for the corresponding estimate under the null hypothesis and alternative. As a result we obtain confidence intervals for the discrepancy of the underlying process from a functional stationary process and a simple asymptotic frequency domain level ® test (using the quantiles of the normal distribution) for the hypothesis of stationarity of functional time series. Moreover, the new methodology allows also to test precise hypotheses of the form “the functional time series is approximately stationarity”, which means that the new measure of stationarity is smaller than a given threshold. Thus in contrast to methods proposed in the literature our approach also allows to test for “relevant” deviations from stationarity. We demonstrate in a small simulation study that the new method has very good finite sample properties and compare it with the currently available alternative procedures. Moreover, we apply our test to annual temperature curves.en
dc.identifier.urihttp://hdl.handle.net/2003/36083
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-18099
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB823;15/2017
dc.subjecttime seriesen
dc.subjectfunctional dataen
dc.subjectspectral analysisen
dc.subjectlocal stationarityen
dc.subjectmeasuring stationarityen
dc.subjectrelevant hypothesesen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleA nonparametric test for stationarity in functional time seriesen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access
eldorado.secondarypublicationfalse

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