Factor Analysis Models for Stationary Stochastic Processes

  • Giorgio Picci
  • Stefano Pinzoni
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 83)


A new class of dynamic models for stationary time series is presented. It is a natural dynamic generalization of the well-known Factor Analysis Model widely used in Statistics. Factor Analysis models of time series are also related to dynalaic Errors-in-Variables models discussed in the recent literature. They provide simple mathematical schemes for the identification of multivariate time series which a-void the unjustified introduction of causality relations among the variables, as for example subsumed by conventional ARNAX models.


Unit Circle Canonical Form Factor Space Minimum Phase Factor Analysis Model 
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  1. 1.
    B.D.O. ANDERSON, “Identification of Scalar Errors-In-Variables Models with Dyna-mics”, Automatica 21, 709–716, 1985.Google Scholar
  2. 2.
    B.D.O. ANDERSON and M. Deistler, “Identifiability in Dynamic Errors-In-Variables Models”, J. Time Series Analysis, 5, 1–13, 1984.Google Scholar
  3. 3.
    H. BART, I. GOHBERG and M.A. KAASHOEK, Minimal Factorization of Matrix and Opera-tor Functions Operator Theory: Advances and Applications, Vol. 1, Birkhäuser Ver-lag, Basel, 1979.zbMATHGoogle Scholar
  4. 4.
    M. DEISTLER, “Identifiability and Causality in Linear Dynamic Errors-In-Variables Systems”, Report, Inst. of Econometrics and Operations Research, University of Technology, Vienna, 1985.Google Scholar
  5. 5.
    L. FINESSO and G. PICCI, “Linear Statistical Models and Stochastic Realization Theory”, in Proc. VI-th Int. Conf. on Analysis and Optimization of Systems Nice, France, June 1984, Springer-Verlag Lect. Nntes in Control and Inf. Sciences 62, 445–470, 1984.Google Scholar
  6. 6.
    P.A. FLERMANN and J C WILLEMS, “Factorization Indices at Infinity for Rational Matrix Functions”, Integral Equations and Operator Theory 2, 287–301, 1979.zbMATHGoogle Scholar
  7. 7.
    I. GOHBERG and M.G. KREIN, “Systems of Integral Equations on a Half Line with Ker-nels Depending on the Difference of Arguments”, Amer. Math. Soc. Transl. (2) 14, 217–287, 1960.Google Scholar
  8. 8.
    R.E. KALMAN, “System Identification from Noisy Data”, in Dynamical Systems II A.R. Bednarek and L. Cesari eds., Academic Press, New York, 1982.Google Scholar
  9. 9.
    R.E. KALMAN, “Identification from Real Data”, in Current Developments in the In-terface: Economics, Econometrics, Mathematics M. Hazewinkel and A.H.G. Rinnooy Kan eds., Reidel, Dordrecht, 1982.Google Scholar
  10. 10.
    R.E. KALMAN, “Identifiability and Modeling in Econometrics”, in Developments in Statistics, Vol.4 P.R. Krishnaiah ed., Academic Press, New York, 1983.Google Scholar
  11. 11.
    A. LINDQUIST and G. PICCI, “Realization Theory for Multivariate Stationary Gaus-sian Processes”, SIAM J. Control and Optimization 23, 809–857, 1985.Google Scholar
  12. 12.
    A. LINDQUIST, G. PICCI and G. RUCKEBUSCH, “On’Minimal Splitting Subspaces and Markoviap Representations”, Math. Systems Theory 12, 271–279, 1979.Google Scholar
  13. 13.
    G. PICCI and S. PINZONI, “A New Class of Dynamic Models for Stationary Time Se-ries”, in Stochastic Models for Time Series S. Bittanti ed., Lect. Notes in Control and Inf. Sci. Snringer-Verlag, Berlin, 1986.Google Scholar
  14. 14.
    G. PICCI and S. PINZONI, “Dynamic Factor Analysis Models for Stationary Processes”, IMA J. Math. Control and Information to appear, 1986.Google Scholar
  15. 15.
    Y.A. ROZANOV, Stationary Random Processes Holden-Day, San Francisco, 1967.Google Scholar
  16. 16.
    G. RUCKEBUSCR, “Representations Markoviennes de Processus Gaussiens Stationnaires” C.R. Acad. Sc. Paris, Ser. A, 282, 649–651, 1976.Google Scholar
  17. 17.
    J.H. VAN XHUPPtN, “Stochastic Realizaticn Problems Motivated by Econometric MO-delAing”, Report 0S-R8507, Centre tor Mathematics and Computer Science, Amsterdam, 1985.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1986

Authors and Affiliations

  • Giorgio Picci
    • 1
  • Stefano Pinzoni
    • 2
  1. 1.Istituto di Elettrotecnica e di ElettronicaPadovaItaly
  2. 2.LADSEB-CNRPadovaItaly

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