Pivotal tests for relevant differences in the second order dynamics of functional time series

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dc.contributor.authorvan Delft, Anne
dc.contributor.authorDette, Holger
dc.date.accessioned2020-10-26T14:19:54Z
dc.date.available2020-10-26T14:19:54Z
dc.date.issued2020
dc.description.abstractMotivated by the need to statistically quantify differences between modern (complex) datasets which commonly result as high-resolution measurements of stochastic processes varying over a continuum, we propose novel testing procedures to detect relevant differences between the second order dynamics of two functional time series. In order to take the between-function dynamics into account that characterize this type of functional data, a frequency domain approach is taken. Test statistics are developed to compare differences in the spectral density operators and in the primary modes of variation as encoded in the associated eigenelements. Under mild moment conditions, we show convergence of the underlying statistics to Brownian motions and obtain pivotal test statistics via a self-normalization approach. The latter is essential because the nuisance parameters can be unwieldly and their robust estimation infeasible, especially if the two functional time series are dependent. Besides from these novel features, the properties of the tests are robust to any choice of frequency band enabling also to compare energy contents at a single frequency. The finite sample performance of the tests are verified through a simulation study and are illustrated with an application to fMRI data.de
dc.identifier.urihttp://hdl.handle.net/2003/39791
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-21682
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB823;10/2020
dc.relation.replaceshttp://hdl.handle.net/2003/39090
dc.subjectfunctional dataen
dc.subjectmartingale theoryen
dc.subjectself-normalizationen
dc.subjectrelevant testsen
dc.subjectspectral analysisen
dc.subjecttime seriesen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.subject.rswkZeitreihede
dc.subject.rswkMartingaletheoriede
dc.titlePivotal tests for relevant differences in the second order dynamics of functional time seriesen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access
eldorado.secondarypublicationfalsede

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