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Stochastic realization and factor analysis

  • J. H. van Schuppen
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 83)

Summary

A general problem of science and engineering is to represent observations by a model. R.E. Kalman [1982,1983] has been voicing a critique of modeling in econometrics. His suggestion is to formulate this modeling problem as a realization problem of system theory.

For the representation of an observed random vector several models have been proposed. Some of these models are: the regression model, the errors-in-variables model, the factor analysis model and the confluence analysis model. From a system theoretic view point only the factor analysis model, or equivalently the confluence analysis model, is acceptable. The key property of this model is the con-ditional independence of the components of the observation vector given the factor.

In this paper the problem will be considered of representing an observation vector in a nondynamic context. The questions in this problem are the existence of a factor model that represents the given observations and the classification of all minimal such models. Only the strong stochastic realization problem for a vector of small dimension will be discussed in some detail.

In a dynamic context where an observed stochastic process has to be modeled, the criticism of econometrics leads to a stochastic realintion problem for a Gaussian process. The novel aspect here is to select a class of stochastic dynamic systems such that the inherent causality relation of the obser-vation process is made explicit. A class of stochastic dynamic systems with which this may be done is proposed and the resulting stochastic realization problem discussed.

References

  1. 1.
    R.E. Kalman (1982). Identification from real data. M. Hazewinkel, A.H.G. Rinnooy Kan (eds.). Current developments in the interface: Economics, Econometrics, Mathematics, D. Reidel Fubl. Co., Dordrecht, 161–196.Google Scholar
  2. 2.
    R.E. Kalman (1983). Identifiability and modeling in econometrics. P.R. Krishnaiah (ed.). Developments in statistics, volume 4, Academic Press, New York, 97–136.Google Scholar
  3. 3.
    G. Picci, S. Pinzoni (1986). Dynamic factor analysis models for stationary processes preprint.Google Scholar
  4. 4.
    J.H. van Schuppen (1985). Stochastic realization problems motivated by econometric modeling, Report 0S - R8507, Centre for Mathematics and Computer Science, Amsterdam.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1986

Authors and Affiliations

  • J. H. van Schuppen
    • 1
  1. 1.Centre for Mathematics and Computer ScienceAB AmsterdamThe Netherlands

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