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)


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.


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    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
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    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
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    G. Picci, S. Pinzoni (1986). Dynamic factor analysis models for stationary processes preprint.Google Scholar
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    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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