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

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Official URL: http://eprints.ucm.es/7653/
Abstract
Although the spectral analysis of stationary stochastic processes has solid mathematical foundations, this is not the case for nonstationary stochastic processes. In this paper, the algebraic foundations of the
spectral analysis of nonstationary 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 pseudocovariance generating function / pseudospectrum, analogous
to the Fourier Transform pair covariance generating function / spectrum, is defined. The new transform pair is well defined for stationary and nonstationary 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 
References: 
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Priestley, M. P. (1981): Spectral Analysis and Time Series, Probability and Mathematical Statistics. Academic Press, London, first edn. Young, P. C., D. Pedregal, and W. Tych (1999): “Dynamic Harmonic Regression,” Journal of Forecasting, 18, 369–394. 
Deposited On:  04 Mar 2008 
Last Modified:  06 Feb 2014 07:55 
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