A Note on the Pseudo-Spectra and the Pseudo-Covariance Generating Functions of ARMA Processes

Andrés Bujosa, Marcos Bujosa and Antonio García Ferrer
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Andrés Bujosa: Universidad Politécnica de Madrid, ETSI Telecomunicación, Dpto. de Matemáticas.
Antonio García Ferrer: Universidad Autónoma de Madrid, Dpto. de Análisis Económico: Economía cuantitativa., https://www.ucm.es/fundamentos-analisis-economico2

Documentos de Trabajo del ICAE from Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico

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.

Pages: pages 18
Date: 2002
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