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Identification of non-linear systems using general state-dependent models

Published online by Cambridge University Press:  14 July 2016

M. B. Priestley  and
S. M. Heravi
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Abstract

This paper describes an extension of the SDM scheme introduced by Priestley (1980) to the problem of the identification of non-linear systems using only input/output records. It is shown that, under quite general assumptions on the structure of the system, it is possible to identify a non-linear relationship between the input and output processes via a modified version of the Kalman-type algorithm previously applied to the study of non-linear time series models. The paper includes a numerical study of data generated from various types of non-linear systems.

Keywords

NON-LINEAR MODELSKALMAN FILTERINGNON-PARAMETRIC FUNCTION FITTING

Information

Type
Part 4—Non-linear and Non-stationary Systems in Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 257 - 272
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Box, G. E. P. and Jenkins, G. M. (1970) Time Series, Forecasting, and Control. Holden-Day, San Francisco.Google Scholar
Brockett, R. W. (1976) Volterra series and geometric control theory. Automatica 12, 167–172.Google Scholar
Granger, C. W. J. and Andersen, A. P. (1978) An Introduction to Bilinear Time Series Models. Vandenhoeck and Ruprecht, Gottingen.Google Scholar
Haggan, V., Heravi, S. M., and Priestley, M. B. (1984) A study of the application of state-dependent models in non-linear time series analysis. J. Time Series Anal. 5, 69–102.CrossRefGoogle Scholar
Haggan, V. and Ozaki, T. (1981) Modelling non-linear random vibrations using an amplitude-dependent autoregressive time series model. Biometrika 68, 189–196.CrossRefGoogle Scholar
Hannan, E. J. (1973) The asymptotic theory of linear time series models. J. Appl. Prob. 10, 130–145.Google Scholar
Hannan, E. J. (1976) The identification and parametrisation of ARMAX and state space forms. Econometrica 44, 713–723.Google Scholar
Hannan, E. J. (1979) Estimating the dimension of a linear system. Paper presented at the International Time Series Meeting, University of Nottingham, England, March 1979.Google Scholar
Hannan, E. J. and Kavalieris, L. (1984) Multivariate linear time series models. Adv. Appl. Prob. 16, 492–561.CrossRefGoogle Scholar
Kalman, R. E. (1963) New methods of Wiener filtering theory. In Proc. 1st Symp. Eng. Appns. of Random Functions Theory and Prob. , ed. Bogdanoff, J. L. and Kozin, F. Wiley, New York.Google Scholar
Kuo, B. C. (1974) Discrete Data Control Systems. Science Tech., Illinois.Google Scholar
Priestley, M. B. (1980) State-dependent models: a general approach to non-linear time series analysis. J. Time Series Anal. 1, 47–71.CrossRefGoogle Scholar
Priestley, M. B. (1981) Spectral Analysis and Time Series , Vols. I and II, Academic Press, London.Google Scholar
Priestley, M. B. and Chao, M. T. (1972) Non-parametric function fitting. J. R. Statist. Soc. B 34, 385–392.Google Scholar
Subba Rao, T. (1981) On the theory of bilinear models. J. R. Statist. Soc. B 43, 244–255.Google Scholar
Tong, H. and Lim, K. S. (1980) Threshold autoregression, limit cycles, and cyclic data. J. R. Statist. Soc. B 42, 245–292.Google Scholar