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. [Working Paper or Technical Report]
Official URL: http://eprints.ucm.es/7653/
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)|
Brockwell, P. J., and R. A. Davis (1987): Time Series: Theory and Methods, Springer series in Statistics. Springer-Verlag, New York.
Bujosa, M., A. Garc´ıa-Ferrer, and P. C. Young (2002): “An ARMA representation of unobserved component models under generalized random walk specifications: new algorithms and examples,”mimeo.
Caines, P. E. (1988): Linear Stochastic Systems, Wiley series in probability and mathematical statistics. John Wiley & Sons, Inc., New York.
Godement, R. (1974): ´ Algebra. Editorial Tecnos, Madrid, first edn. Harvey, A. (1989): Forecasting Structural Time Series Models and the Kalman Filter. Cambridge University Press, Cambridge, first edn.
Hatanaka, M., and M. Suzuki (1967): “A theory of the Pseudosprectrum and Its Application to Nonstationary Dynamic Ecomometric Models,” in Essays in Mathematical Economics. In Honor of Oskar Morgenstern, ed. by M. Shubik, chap. 26, pp. 443–446. Princeton University Press, Princeton, New Jersey.
Luenberger, D. G. (1968): Optimization by vector space methods, Series in decision and control. John Wiley & Sons, Inc., New York.
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:||15 Nov 2013 11:49|
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