Template-type: ReDIF-Paper 1.0
Author-Name: Andrés Bujosa 
Author-Workplace-Name: Universidad Politécnica de Madrid, ETSI Telecomunicación, Dpto. de Matemáticas.
Author-Name: Marcos Bujosa 
Author-Email: marcos.bujosa@ccee.ucm.es
Author-Person: pbu154 
Author-Homepage:
 https://www.ucm.es/fundamentos-analisis-economico2/marcos-bujosa
Author-Workplace-Name: Universidad Complutense de Madrid, Dpto. de Fundamentos del Análisis Económico II.
Author-Workplace-Homepage:
 https://www.ucm.es/fundamentos-analisis-economico2
Author-Name: Antonio García Ferrer
Author-Workplace-Name: Universidad Autónoma de Madrid, Dpto. de Análisis Económico: Economía cuantitativa. 
Author-Workplace-Homepage:
 https://www.ucm.es/fundamentos-analisis-economico2
Title: A Note on the Pseudo-Spectra and the Pseudo-Covariance Generating Functions of ARMA Processes
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.
Length: pages 18
Creation-Date: 2002
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae0203.txt
File-URL: https://eprints.ucm.es/id/eprint/7653/1/0203.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doicae:0203