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Título:
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Mathematical framework for pseudo-spectra of linear stochastic difference equations
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Autores:
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Bujosa Brun, Marcos ;
Bujosa Brun, Andrés ;
García Ferrer, Antonio
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Tipo de documento:
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texto impreso
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Editorial:
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Facultad de CC Económicas y Empresariales. Instituto Complutense de Análisis Económico (ICAE), 2015
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = No publicado
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Materia = Ciencias Sociales: Economía: Econometría
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Tipo = Documento de trabajo o Informe técnico
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Resumen:
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Although 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.
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En línea:
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https://eprints.ucm.es/id/eprint/20699/1/1313.pdf
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