A note on Herglotz’s theorem for time series on function spaces

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dc.contributor.authorvan Delft, Anne
dc.contributor.authorEichler, Michael
dc.date.accessioned2019-09-06T13:29:27Z
dc.date.available2019-09-06T13:29:27Z
dc.date.issued2019
dc.description.abstractIn this article, we prove Herglotz’s theorem for Hilbert-valued time series. This requires the notion of an operator-valued measure, which we shall make precise for our setting. Herglotz’s theorem for functional time series allows to generalize existing results that are central to frequency domain analysis on the function space. In particular, we use this result to prove the existence of a functional Cramér representation of a large class of processes, including those with jumps in the spectral distribution and long-memory processes. We furthermore obtain an optimal finite dimensional reduction of the time series under weaker assumptions than available in the literature. The results of this paper therefore enable Fourier analysis for processes of which the spectral density operator does not necessarily exist.en
dc.identifier.urihttp://hdl.handle.net/2003/38207
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-20186
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB823;20/2019
dc.subjectfunctional data analysisen
dc.subjecttime seriesen
dc.subjectspectral analysisen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleA note on Herglotz’s theorem for time series on function spacesen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access
eldorado.secondarypublicationfalsede

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