Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T16:38:47.019Z Has data issue: false hasContentIssue false

Linear dynamic errors-in-variables models

Published online by Cambridge University Press:  14 July 2016

Abstract

Linear dynamical systems where both inputs and outputs are contaminated by errors are considered. A characterization of the sets of all observationally equivalent transfer functions is given, the role of the causality assumption is investigated and conditions for identifiability in the case of Gaussian as well as non-Gaussian observations are derived.

Type
Part 1—Structure and General Methods for Time Series
Copyright
Copyright © 1986 Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aigner, D. J., Hsiao, C., Kapteyn, A. and Wansbeek, T. (1984) Latent variable models in econometrics. In Handbook of Econometrics , ed. Grilliches, Z. and Intriligator, M. D., North-Holland, Amsterdam.Google Scholar
Akaike, H. (1966) On the use of non-Gaussian process in the identification of a linear dynamic system. Ann. Inst. Statist. Math. 18, 269276.CrossRefGoogle Scholar
Anderson, B. D. O. (1985) Identification of scalar errors-in-variables models with dynamics. Automatica. To appear.Google Scholar
Anderson, B. D. O. and Deistler, M. (1984) Identifiability in dynamic errors-in-variables models. J. Time Series Anal. 5, 113.Google Scholar
Anderson, T. W. (1984) Estimating linear statistical relationships. Ann. Statist. 12, 145.Google Scholar
Brillinger, D. R. (1981) Time Series: Data Analysis and Theory. Holden Day, San Francisco.Google Scholar
Deistler, M. and Seifert, H. G. (1978) Identifiability and consistent estimability in dynamic econometric models. Econometrica 46, 969980.Google Scholar
Frisch, R. (1934) Statistical Confluence Analysis by Means of Complete Regression Systems. Publication No. 5, University of Oslo, Economic Institute.Google Scholar
Geary, R. C. (1942) Inherent relations between random variables. Proc. R. Irish Acad. A 47, 6376.Google Scholar
Hannan, E. J. (1963) Regression for time series with errors of measurement. Biometrika 50, 293302.Google Scholar
Hannan, E. J. (1969) The identification of vector mixed autoregressive-moving average systems. Biometrika 56, 223225.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.CrossRefGoogle Scholar
Hannan, E. J. (1971) The identification problem for multiple equation systems with moving average errors. Econometrica 39, 751765.CrossRefGoogle Scholar
Hannan, E. J. (1976) The identification and parametrization of ARMAX and state space forms. Econometrica 44, 713723.Google Scholar
Hannan, E. J. and Kavalieris, L. (1984) Multivariate linear time series models. Adv. Appl. Prob. 16, 492561.Google Scholar
Kalman, R. E. (1982) System identification from noisy data. In Dynamical Systems II, a University of Florida International Symposium, eds. Bednarek, A. and Cesari, L. Academic Press, New York.Google Scholar
Kalman, R. E. (1983) Identifiability and modeling in econometrics. In Developments in Statistics 4, ed. Krishnaiah, P. R. Academic Press, New York.Google Scholar
Madansky, A. (1959) The fitting of straight lines with both variables are subject to error. J. Amer. Statist. Assoc. 54, 173205.Google Scholar
Maravall, A. (1979) Identification in Dynamic Shock-Errors Models. Springer-Verlag, Berlin.Google Scholar
Moran, P. A. P. (1971) Estimating structural and functional relationships. J. Multivariate Anal. 1, 232255.CrossRefGoogle Scholar
Nowak, E. (1983) Identification of the dynamic shock-error model with autocorrelated errors. J. Econometrics 23, 211221.Google Scholar
Reisersøl, O. (1950) Identifiability of a linear relation between variables which are subject to error. Econometrica 9, 124.Google Scholar
Wegge, L. (1982) ARMAX-Model parameter identification without and with latent variables. Working Paper. Dept. of Economics, Univ. of California, Davis.Google Scholar