Mathematical framework for pseudo-spectra of linear stochastic difference equations

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dc.contributor.authorBujosa Brun, Marcos
dc.contributor.authorBujosa Brun, Andrés
dc.contributor.authorGarcía Ferrer, Antonio
dc.date.accessioned2023-06-19T23:52:50Z
dc.date.available2023-06-19T23:52:50Z
dc.date.issued2013
dc.descriptionThis working paper has been accepted for publication in a future issue of IEEE Transactions on Signal Processing. Content may change prior to final publication. Citation information: DOI:10.1109/TSP.2015.2469640. 1053-587X copy right 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
dc.description.abstractAlthough spectral analysis of stationary stochastic processes has solid mathematical foundations, this is not always so for some non-stationary cases. Here, we establish a rigorous mathematical extension of the classic Fourier spectrum to the case in which there are AR roots in the unit circle, ie, the transfer function of the linear time-invariant filter has poles on the unit circle. To achieve it we: embed the classical problem in a wider framework, the Rigged Hilbert space, extend the Discrete Time Fourier Transform and defined a new Extended Fourier Transform pair pseudo-covariance function/pseudo-spectrum. Our approach is a proper extension of the classical spectral analysis, within which the Fourier Transform pair auto-covariance function/spectrum is a particular case. Consequently spectrum and pseudo-spectrum coincide when the first one is defined.
dc.description.facultyFac. de Ciencias Económicas y Empresariales
dc.description.facultyInstituto Complutense de Análisis Económico (ICAE)
dc.description.refereedFALSE
dc.description.statusunpub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/20699
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dc.identifier.relatedurlhttps://www.ucm.es/icae
dc.identifier.urihttps://hdl.handle.net/20.500.14352/41468
dc.issue.number13
dc.language.isoeng
dc.page.total15
dc.publisherFacultad de CC Económicas y Empresariales. Instituto Complutense de Análisis Económico (ICAE)
dc.relation.ispartofseriesDocumentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)
dc.rights.accessRightsopen access
dc.subject.jelC00
dc.subject.jelC22
dc.subject.keywordSpectral analysis
dc.subject.keywordtime series
dc.subject.keywordnon-stationarity
dc.subject.keywordfrequency domain
dc.subject.keywordpseudo-covariance function
dc.subject.keywordlinear stochastic difference equations
dc.subject.keywordRigged Hilbert space
dc.subject.keywordpartial inner product
dc.subject.keywordExtended Fourier Transform.
dc.subject.ucmEconometría (Economía)
dc.subject.unesco5302 Econometría
dc.titleMathematical framework for pseudo-spectra of linear stochastic difference equations
dc.typetechnical report
dc.volume.number2013
dspace.entity.typePublication
relation.isAuthorOfPublication3e6ecbfe-83ad-404d-8f47-b6e76491c702
relation.isAuthorOfPublication.latestForDiscovery3e6ecbfe-83ad-404d-8f47-b6e76491c702
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