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A note on the pseudo-spectra and the pseudo-covariance generating functions of ARMA processes


Bujosa Brun, Andrés y Bujosa Brun, Marcos y García Ferrer , Antonio (2002) A note on the pseudo-spectra and the pseudo-covariance generating functions of ARMA processes. [ Documentos de trabajo del Instituto Complutense de Análisis Económico (ICAE); nº 0203, 2002, ]

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Although the spectral analysis of stationary stochastic processes has solid mathematical foundations, this is not the case for non-stationary stochastic processes. In this paper, the algebraic foundations of the
spectral analysis of non-stationary ARMA processes are established.
For this purpose the Fourier Transform is extended to the field of fractions of polynomials. Then, the Extended Fourier Transform pair pseudo-covariance generating function / pseudo-spectrum, analogous
to the Fourier Transform pair covariance generating function / spectrum, is defined. The new transform pair is well defined for stationary and non-stationary ARMA processes. This new approach can be
viewed as an extension of the classical spectral analysis. It is shown that the frequency domain has some additional algebraic advantages
over the time domain.

Tipo de documento:Documento de trabajo o Informe técnico
Palabras clave:Fourier Transform
Materias:Ciencias Sociales > Economía > Econometría
Título de serie o colección:Documentos de trabajo del Instituto Complutense de Análisis Económico (ICAE)
Código ID:7653

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Depositado:04 Mar 2008
Última Modificación:06 Feb 2014 07:55

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