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

Bujosa Brun, Andrés and Bujosa Brun, Marcos and 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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Abstract

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.


Item Type:Working Paper or Technical Report
Uncontrolled Keywords:Fourier Transform
Subjects:Social sciences > Economics > Econometrics
Series Name:Documentos de trabajo del Instituto Complutense de Análisis Económico (ICAE)
Volume:2002
Number:0203
ID Code:7653
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Deposited On:04 Mar 2008
Last Modified:06 Feb 2014 07:55

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