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Consistency of System Identification by Global Total Least Squares

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  • Heij, C.
  • Scherrer, W.

Abstract

Global total least squares (GTLS) is a method for the identification of linear systems where no distinction between input and output variables is required. This method has been developed within the deterministic behavioural approach to systems. In this paper we analyse statistical properties of this method when the observations are generated by a multivariable stationary stochastic process. In particular, sufficient conditions for the consistency of GTLS are derived. This means that, when the number of observations tends to infinity, the identified deterministic system converges to the system that provides an optimal appoximation of the data generating process. The two main results are the following. GTLS is consistent if a guaranteed stability bound can be given a priori. If this information is not available, then consistency is obtained (at some loss of finite sample efficiency) if GTLS is applied to the observed data extended with zero values in past and future.

Suggested Citation

  • Heij, C. & Scherrer, W., 1996. "Consistency of System Identification by Global Total Least Squares," Econometric Institute Research Papers EI 9635-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1387
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    References listed on IDEAS

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    1. Heij, C. & Scherrer, W. & Destler, M., 1996. "System Identification by Dynamic Factor Models," Econometric Institute Research Papers EI 9501-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Heij, C. & Scherrer, W., 1995. "Consistency of global total least squares in stochastic system identification," Econometric Institute Research Papers EI 9522-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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    Cited by:

    1. Scherrer, W. & Heij, C., 1997. "Identification of System Behaviours by Approximation of Time Series Data," Econometric Institute Research Papers EI 9710-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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    1. Heij, C. & Scherrer, W., 1996. "Behavioural Approximation of Stochastic Processes by Rank Reduced Spectra," Econometric Institute Research Papers EI 9610/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Heij, C. & Scherrer, W. & Destler, M., 1996. "System Identification by Dynamic Factor Models," Econometric Institute Research Papers EI 9501-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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