Of copulas, quantiles, ranks and spectra an L1-approach to spectral analysis

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dc.contributor.authorDette, Holger
dc.contributor.authorHallin, Marc
dc.contributor.authorKley, Tobias
dc.contributor.authorVolgushev, Stanislav
dc.date.accessioned2011-12-06T11:52:17Z
dc.date.available2011-12-06T11:52:17Z
dc.date.issued2011-12-06
dc.description.abstractIn this paper we present an alternative method for the spectral analysis of a strictly stationary time series (Yt)eZ. We define a "new" spectrum as the Fourier transform of the differences between copulas of the pairs (Yt; Yt-k) and the independence copula. This object is called copula spectral density kernel and allows to separate marginal and serial aspects of a time series. We show that it is intrinsically related to the concept of quantile regression. Like in quantile regression, which provides more information about the conditional distribution than the classical location-scale model, the copula spectral density kernel is more informative than the spectral density obtained from the autocovariances. In particular the approach provides a complete description of the distributions of all pairs (Yt; Yt-k). Moreover, it inherits the robustness properties of classical quantile regression, because it does not require any distributional assumptions such as the existence of fi nite moments. In order to estimate the copula spectral density kernel we introduce rank-based Laplace periodograms which are calculated as bilinear forms of weighted L1-projections of the ranks of the observed time series onto a harmonic regression model. We establish the asymptotic distribution of those periodograms, and the consistency of adequately smoothed versions. The finite-sample properties of the new methodology, and its potential for applications are briefly investigated by simulations and a short empirical example.de
dc.identifier.urihttp://hdl.handle.net/2003/29220
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-3252
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB 823;47/2011
dc.subjectCopulasen
dc.subjectPeriodogramen
dc.subjectQuantile regressionen
dc.subjectRanksen
dc.subjectSpectral analysisen
dc.subjectTime reversibilityen
dc.subjectTime seriesen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleOf copulas, quantiles, ranks and spectra an L1-approach to spectral analysisen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access

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Sonderforschungsbereich (SFB) 823