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Identification of transfer function matrix using higher-order spectra

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Abstract

This paper treats of the identification of parametric transfer function matrix. The method is based on the inner-outer factorization of a stable transfer function matrix. The outer part is identified by the use of the second-order spectral estimate, from the observed linear process, while the inner part is identified by the use of a higher-order cumulant spectral estimate, from the observed process. Respective parameter estimators are determined in the light of asymptotic efficiency. In order to estimate the order of the inner part, a criterion IIC is introduced based on the same principle as in the case of Akaike’s AIC.

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References

  1. H. Akaike, A new look at the statistical model identification. IEEE Trans. Automat. Control,19 (1974), 716–723.

    Article  MATH  MathSciNet  Google Scholar 

  2. D.R. Brillinger, Time Series: Data Analysis and Theory. Holt, New York, 1975.

    MATH  Google Scholar 

  3. D.R. Brillinger and M. Rosenblatt, Asymptotic theory of estimates ofk-th order spectra. Spectral Analysis of Time Series (ed. B. Harris), Wiley, New York, 1967, 153–188.

    Google Scholar 

  4. D.R. Brillinger and M. Rosenblatt, Computation and interpretation ofk-th order spectra. Spectral Analysis of Time Series (ed. B. Harris), Wiley, New York, 1967, 189–232.

    Google Scholar 

  5. P. Kabaila, On estimating time series parameters using sample auto correlations. J. Roy. Statist. Soc. Ser. B,45 (1983), 107–119.

    MATH  MathSciNet  Google Scholar 

  6. D.M. Keenan, Asymptotic properties of minimization estimators for time series parameters. Ann. Statist.,13 (1985), 369–382.

    Article  MATH  MathSciNet  Google Scholar 

  7. D.M. Keenan, Limiting behavior of functionals of higher-order sample cumulant spectra. Ann. Statist.,15 (1987), 134–151.

    Article  MathSciNet  Google Scholar 

  8. M. Kumon, Identification of non-minimum phase transfer function using higher-order spectrum. Ann. Inst. Statist. Math.44 (1992), 239–260.

    Article  MATH  MathSciNet  Google Scholar 

  9. K.S. Lii and M. Rosenblatt, Deconvolution and estimation of transfer function phase and coefficients for non-Gaussian linear processes. Ann. Statist.,10, (1982), 1195–1208.

    Article  MATH  MathSciNet  Google Scholar 

  10. B. Sz.-Nagy and C. Foias, Harmonic Analsis of Operators on Hilbert Space. American Elsevier, New York, 1970.

    Google Scholar 

  11. M. Rosenblatt, Linear processes and bispectra. J. Appl. Probab.17 (1980), 265–270.

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. 272-1 Ohaza-aida, 820, Iizuka city, Fukuoka pref., Japan

    Masayuki Kumon

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  1. Masayuki Kumon
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Kumon, M. Identification of transfer function matrix using higher-order spectra. Japan J. Indust. Appl. Math. 13, 217–233 (1996). https://doi.org/10.1007/BF03167244

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  • DOI: https://doi.org/10.1007/BF03167244

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