EconStor >
Universität zu Köln >
Institut für Ökonometrie und Statistik, Universität Köln >
Discussion Papers in Econometrics and Statistics, Institut für Ökonometrie und Statistik, Universität Köln >

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10419/26740
  

Full metadata record

DC FieldValueLanguage
dc.contributor.authorFrahm, Gabrielen_US
dc.contributor.authorJaekel, Uween_US
dc.date.accessioned2007-04-25en_US
dc.date.accessioned2009-07-29T14:23:20Z-
dc.date.available2009-07-29T14:23:20Z-
dc.date.issued2007en_US
dc.identifier.urihttp://hdl.handle.net/10419/26740-
dc.description.abstractIn recent publications standard methods of random matrix theory were applied to principal components analysis of high-dimensional financial data. We discuss the fundamental results and potential shortcomings of random matrix theory in the light of the stylized facts of empirical finance. Especially, our arguments are based on the impact of nonlinear dependencies such as tail dependence. After a brief discussion of the stylized facts we present the class of multivariate generalized elliptical distributions. This class allows for the modeling of various anomalies frequently observed in financial data. Thus it will serve as a general model for the investigation of standard methods of random matrix theory. It is shown that the Marčenko-Pastur law generally fails when analyzing the empirical distribution function of the eigenvalues given by the sample covariance matrix of generalized elliptically distributed data. As an alternative we derive a random matrix referred to as the spectral estimator which is distribution-free within the class of generalized elliptical distributions. Moreover, we show that the spectral estimator corresponds to Tyler's M-estimator and many important properties of the spectral estimator can be obtained from the corresponding literature. Substituting the sample covariance matrix by the spectral estimator resolves the problems which are due to the stylized facts and the Marčenko-Pastur law remains valid. This holds even if the data are not generalized elliptically distributed but mutually independent.en_US
dc.language.isoengen_US
dc.publisherUniv., Seminar für Wirtschafts- und Sozialstatistik Kölnen_US
dc.relation.ispartofseriesDiscussion papers in statistics and econometrics 2/07en_US
dc.subject.ddc330en_US
dc.subject.stwZeitreihenanalyseen_US
dc.subject.stwMatrizenrechnungen_US
dc.subject.stwSchätztheorieen_US
dc.subject.stwFinanzmarkten_US
dc.subject.stwStatistische Verteilungen_US
dc.subject.stwTheorieen_US
dc.titleTyler's M-estimator, random matrix theory, and generalized elliptical distributions with applications to financeen_US
dc.typeWorking Paperen_US
dc.identifier.ppn527784575en_US
dc.rightshttp://www.econstor.eu/dspace/Nutzungsbedingungen-
dc.identifier.repecRePEc:zbw:ucdpse:207-
Appears in Collections:Discussion Papers in Econometrics and Statistics, Institut für Ökonometrie und Statistik, Universität Köln

Files in This Item:
File Description SizeFormat
527784575.PDF1.19 MBAdobe PDF
No. of Downloads: Counter Stats
Show simple item record
Download bibliographical data as: BibTeX

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.